Geostatistical Risk Analysis of Static and Dynamic Crime

GEOSTATISTICAL RISK ANALYSIS OF STATIC AND DYNAMIC CRIME

Nikki Filipuzzi M.A., Simon Fraser University, 2003 B.A., Mount Royal University, 2001

DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

DOCTOR OF PHILOSOPHY

In the School of Criminology

SIMON FRASER UNIVERSITY

FALL 2010

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The author, whose name appears on the title page of this work, has obtained, for the research described in this work, either: (a) Human research ethics approval from the Simon Fraser University Office of Research Ethics, or (b) Advance approval of the animal care protocol from the University Animal Care Committee of Simon Fraser University; or has conducted the research (c) as a co-investigator, collaborator or research assistant in a research project approved in advance, or (d) as a member of a course approved in advance for minimal risk human research, by the Office of Research Ethics. A copy of the approval letter has been filed at the Theses Office of the University Library at the time of submission of this thesis or project. The original application for approval and letter of approval are filed with the relevant offices. Inquiries may be directed to those authorities.

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Last update: Spring 2010 ABSTRACT

The Geography of Crime has a history in criminology that repeatedly finds a clustering of crime in time and space. Research in this field explores spatio- temporal patterning by studying who commits crimes, and why and when they commit crimes more in some parts of a city. Research finds a level of stability for many crimes.

This thesis uses reported assault and break-and-enter crimes in Regina to explore in more depth the spatial-temporal patterns of crime and to develop and use hazard-risk modelling to improve methods of predicting future crime concentrations. Specifically, in order to explore and improve current hazard-risk models in criminology, new software was created for this thesis (Crime Risk

Assessment Software). This software allows for the generation of a geostatistical risk model of two crime types, assault and break-and-enter (dynamic and static, respectively), to determine whether geostatistics, specifically Kriging techniques, could create strong predictive risk surfaces of these crimes.

Through this exploratory spatio-temporal research, it was believed that after buildling and testing the model, statistics would reveal that the Kriging model would more accurately predict static crime than it would dynamic crime owing to the mobility issue of the crimes chosen (e.g., assault can happen anywhere spatially whereas break-and-enter can only occur at a static location such as a residence).

iii Using examples provided by the Regina Police Service (RPS) in

Saskatchewan, Canada, from assault and break-and-enter data gathered over the period from January 1, 2005, to December 31, 2005, both the Kriging risk models and the Crime Risk Assessment software demonstrated successful application in depicting spatially clustered data consistent with Geography of

Crime Geography of Crime research.

Keywords: Spatial Analysis, Geostatistical Analysis, Crime, Break & Enter, Assault, Kriging, Geographic Information Systems (GIS);

iv DEDICATION

I would like to dedicate this to the most supportive and loving family in the world.

To my husband Jamie Filipuzzi, who never stopped believing in me. To my

parents, Sandy and Terry Thompson, who are the most helpful and

understanding parents a child could ever have. Most of all, to my children,

Damyn and Mataya, for without you both I would not have had the inspiration to

finish this arduous task. I am truly blessed to have had such amazing family

support.

v ACKNOWLEDGEMENTS

This thesis would have never come to fruition without the help and support of many people. First and foremost, I would like to thank my committee for their support: Dr. Patricia L Brantingham, School of Criminology, Simon Fraser

University; Professor Bill Glackman, School of Criminology, Simon Fraser

University; and Dr. John Winterdyk, Department of Justice Studies, Mount Royal

University. My committee provided me with encouragement and tremendous support for which I am extremely appreciative.

I would like to extend a special thanks to the Regina Police Service for the use of their data for this thesis. In particular, I would like to thank Jennifer

Clarke, Strategic Research Officer, Regina Police Service, and Sgt. Rick

Bourassa, Regina Police Service. I would also like to acknowledge the dedicated work of our software development team. In particular, Dr. Peter Zizler, Software

Designer, Mount Royal University; Patti Derbyshire, Project Manager, Mount

Royal University, Dr. John Winterdyk, Department of Justice Studies, Mount

Royal University; Laura Markin, Programmer, Mount Royal University; Dave

Dever, Programmer, Mount Royal University; Steven Pridgen, Research Student,

Mount Royal University; and a special thanks to Natalie O’Toole, GIS Specialist,

Mount Royal University who’s GIS knowledge and support was invaluable. And also a special thank you to my editor, JoAnn Cleaver whose expertise was extremely helpful.

vi TABLE OF CONTENTS

Approval ...... ii Abstract ...... iii Dedication ...... v Acknowledgements ...... vi Table of Contents ...... vii List of Figures ...... x List of Tables ...... xii List of Equations ...... xiii Glossary ...... xiv 1: Introduction ...... 1 2: Risk & Hazard Modelling ...... 6 2.1 Defining Risk, Hazard, and Vulnerability ...... 6 2.2 Risk & Hazard Model Applications ...... 9 2.3 Examples of Risk and Hazard Models in Public Safety ...... 16 2.4 Case Application of Geostatistics ...... 24 3: Theoretical Foundations for Spatial Analysis ...... 29 3.1 Levels of Environmental Theory – Micro, Meso and Macro ...... 30 3.2 Geography of Crime ...... 32 3.2.1.1 Routine Activity ...... 37 3.2.1.2 Crime Pattern Theory ...... 38 3.3 Summary & Application ...... 40

4: Case Study ...... 42 4.1 Static & Dynamic Crimes ...... 43 4.1.1 Residential Break & Enter ...... 44 4.1.1.1 Geo-Spatial Information (Target Selection) ...... 47 4.1.1.2 Dwelling Characteristics (Situation) ...... 49 4.1.1.3 Temporal Aspects ...... 52 4.1.2 Assault ...... 55 4.1.2.1 Spatial Dynamics of Assault ...... 55 4.1.2.2 Temporal & Temperature Characteristics of Assault ...... 58 4.1.2.3 Demographic Characteristics ...... 60 4.1.3 Summary ...... 60

vii 4.2 Methods & Procedures ...... 61 4.2.1 Sample & Study Area Overview ...... 61 4.2.1.1 Data Privacy and Confidentiality ...... 65 4.2.1.2 Overview of Regina, SK ...... 66 4.2.2 Software ...... 68 4.2.2.1 Geographical Crime Risk Assessment Software ...... 69 4.2.2.2 ArcGIS ...... 72 4.2.3 Techniques and Procedures ...... 74 4.2.4 Statistical Analysis ...... 75 4.2.5 Point Data ...... 76 4.2.5.1 Visual Analysis ...... 77 4.2.5.2 & ...... 78 4.2.5.3 Nearest Neighbour ...... 80 4.2.5.4 Spatial Autocorrelation (SAC) ...... 81 4.2.5.5 Spatial Intensity Plots ...... 82 4.2.5.6 Standard Deviational Ellipses (SDEs) ...... 83 4.2.5.7 Kriging ...... 86 4.2.6 Polygon Data ...... 91 4.2.6.1 Descriptive...... 91 4.2.6.2 Neighbours ...... 91 4.2.6.3 Spatial Autocorrelation ...... 92 4.2.7 Summary ...... 95 4.3 Results ...... 95 4.4 Point Data Results ...... 96 4.4.1 Assault Point Data Results ...... 97 4.4.1.1 Assault Temporal Results ...... 97 4.4.1.2 Complete Spatial Randomness (CSR) ...... 98 4.4.1.3 Nearest Neighbour Index (nna) ...... 99 4.4.1.4 Intensity and Surface Plots ...... 103 4.4.1.5 Standard Deviational Ellipses and Mean Centre Analysis ...... 108 4.4.1.6 Kriging ...... 111 4.4.2 Break-and-Enter Point Data Results ...... 119 4.4.2.1 Break-and-Enter Temporal Results ...... 119 4.4.2.2 Complete Spatial Randomness (CSR) ...... 120 4.4.2.3 Nearest Neighbour Analysis (Nna) and Autocorrelation ...... 122 4.4.2.4 Intensity and Surface Plots ...... 126 4.4.2.5 Standard Deviational Ellipses and Mean Centre Analysis ...... 130 4.4.2.6 Kriging ...... 134 4.5 Polygon Data Results ...... 142 4.5.1 Assault Data Polygon Results ...... 142 4.5.1.1 Spatial Neighbours ...... 144 4.5.1.2 Spatial Autocorrelation ...... 145 4.5.2 Break-and-Enter Data Polygon Results ...... 149 4.5.2.1 Spatial Neighbours ...... 151 4.5.2.2 Spatial Autocorrelation ...... 151 4.6 Assault and Break-and-Enter Comparative Results ...... 156 4.6.1.1 Standard Deviational Ellipses and Mean Centre Analysis ...... 156

viii 4.6.1.2 Kriging ...... 160

5: Discussion ...... 164 5.1 Findings ...... 165 5.1.1 Temporal Findings ...... 165 5.1.2 Comprehensive Model Overviews ...... 169 5.1.2.1 Regina Crime Context ...... 177 5.2 Public Safety Implications ...... 183 5.2.1 Risk and Hazard Model Uses ...... 184 5.2.2 Risk and Hazard Model Misuses ...... 187 5.2.3 Current Implications ...... 191 6: Conclusion ...... 193 7: Appendix A: Data Sharing Agreement ...... 197 8: References ...... 204

ix LIST OF FIGURES

Figure 1 Catastrophe Loss Model ...... 22 Figure 2 Dasymetric Mapping ...... 23 Figure 3 Distance Decay Re-Examined (Rengert et al., 1999 435) ...... 47 Figure 4 Reproduction of “The Decision Process in Target Selection” (Cromwell et al., 1991, 39) ...... 52 Figure 5 Total Assault in Regina 2005, by the Hour ...... 97 Figure 6 Complete Spatial Randomness of Assault Data ...... 99 Figure 7 Nearest Neighbour Analysis of Assault ...... 102 Figure 8 Intensity and Surface Assault Plots...... 105 Figure 9 Assault Total Incidents in Regina 2005 ...... 107 Figure 10 Standard Deviational Ellipses for All Assault Data ...... 110 Figure 11 Assault 70% and 30% Point...... 112 Figure 12 Assault Model Triangulation...... 113 Figure 13 Assault Kriging Clusters ...... 114 Figure 14 Assault Smoothed Kriging Surfaces ...... 116 Figure 15 Assault Model and Test Group Kriging Correlation ...... 118 Figure 16 Total Break-and-Enters by the Hour in Regina, 2005 ...... 119 Figure 17 Complete Spatial Randomness for Break-and-Enters ...... 121 Figure 18 Nearest Neighbour Results for Break-and-Enter ...... 124 Figure 19 Break-and-Enter Intensity Plots ...... 127 Figure 20 Break-and-Enter Total Incidents ...... 129 Figure 21 Break-and-Enter Standard Deviational Ellipses ...... 133 Figure 22 Kriging Break-and-Enter Point Data ...... 135 Figure 23 Break-and-Enter Kriging Triangulation ...... 136 Figure 24 Break-and-Enter Kriging Clusters ...... 137 Figure 25 Break-and-Enter Smoothed Kriging Surfaces ...... 139 Figure 26 Break-and-Enter Kriging Correlation ...... 141 Figure 27 Getis-Ord General G High/Low Clustering Test Assault ...... 145 Figure 28 Spatial Autocorrelation of Assault ...... 146

x Figure 29 Spatial Autocorrelation of Assault Full, Model and Test Groups ...... 148 Figure 30 Getis-Ord General G High/Low Clustering Test for Break-and-Enter ...... 151 Figure 31 Spatial Autocorrelation for Break-and-Enter ...... 153 Figure 32 Spatial Autocorrelation for Break-and-Enter Full, Model and Test Groups ...... 155 Figure 33 Standard Deviational Ellipses for Assault and Break-and-Enter ...... 159 Figure 34 Assault and Break-and-Enter Kriging Correlation ...... 162 Figure 35 Kernel Density Distribution of Violent Incidents, Regina, 2001 (Wallace et al., 2006, 12) ...... 168 Figure 36 Comprehensive Model of Assault ...... 170 Figure 37 Comprehensive Model of Break & Enter ...... 175 Figure 38 Reproduced Chart: “Land-use and Housing Characteristics for Violent Crime” (Wallace et al., 2006, 17) ...... 178 Figure 39 Population Characteristics for Violent Crime (Wallace et al., 2006, 18) ...... 179 Figure 40 Socio-economic Characteristics for Violent Crime (Wallace et al., 2006, 19) ...... 180 Figure 41 Population Characteristics for Property Crime (Wallace et al., 2006, 19) ..... 181 Figure 42 Land-use and Housing Characteristics for Property Crime (Wallace et al., 2006, 18) ...... 182 Figure 43 Socio-economic Characteristics of Property Crime (Wallace et al., 2006, 20) ...... 183

xi LIST OF TABLES

Table 1 Model and Test Databases for Assault and Break and Enter Single Point Data ...... 63 Table 2 Model and Test Databases for Assault and Break-and-Enter Aggregate Point Data ...... 64 Table 3 Nearest Neighbour Results for Assault ...... 100 Table 4 Spatial Autocorrelation of Point Data for Assault in Regina 2005 ...... 103 Table 5 Mean Centre Assault Results ...... 108 Table 6 Length and Area of Standard Deviational Ellipses for Assault ...... 109 Table 7 Nearest Neighbour Statistics for Break-and-Enter...... 123 Table 8 Spatial Autocorrelation of Break-and-Enter Point Data ...... 125 Table 9 Mean Centre Break-and-Enter Results ...... 131 Table 10 Length and Area of Standard Deviational Ellipses for Break-and-Enters ...... 131 Table 11 Assault Counts by Neighbourhood in Regina 2005 ...... 143 Table 12 Break-and-Enter Counts, by Neighbourhood ...... 150 Table 13 Mean Centre for Assault and Break-and-Enter ...... 157 Table 14 Length and Area of Standard Deviational Ellipses, Assault and Break- and-Enter ...... 158 Table 15 A Sample of Risks Subject to Government Intervention (Hill & Dinsdale, 2001, 46) ...... 186

xii LIST OF EQUATIONS

Equation 1 Risk Calculation (Tobin & Montz, 1997) ...... 10 Equation 2 Kernel Density Estimation (Brunsdon, 1995, 878) ...... 25 Equation 3 Adaptive Kernel Density Estimation (Brunsdon, 1995, 880) ...... 26 Equation 4 Kriging Estimator Function (Diggle et al., 1998, 299) ...... 27 Equation 5 Centroid Calculation (Zizler, 2008, 2) ...... 70 Equation 6 Midpoint Calculation (Zizler, 2008) ...... 70 Equation 7 (Wimble et al., 2006) ...... 79 Equation 8 Nearest Neighbour Distance (Rogerson, 2001, 161)...... 81 Equation 9 Moran’s I Statistic. Source: (Fortin et al., 2002, 5) ...... 82 Equation 10 Standard Deviational Ellipse (Levine, 2004) ...... 84 Equation 11 Mean Centre Equation (Levine, 2004, 4.4) ...... 85 Equation 12 Kriging Estimator Function (Diggle et al., 1998, 299) ...... 88 Equation 13 Moran’s I Statistic. Source: (Fortin et al., 2002, 5) ...... 94

xiii GLOSSARY

CAD Computer Assisting Dispatch

CPTED Crime Prevention through Environmental Design

CSR Complete Spatial Randomness

DBF Digital Boundary File

ESDA Exploratory Spatial Data Analysis

GIS Geographic Information Systems

LISA Local Indicators of Spatial Association

MAUB Modifiable Areal Unit Boundary

NNA Nearest Neighbour Analysis

SAC Spatial Autocorrelation

SDE Standard Deviational Ellipses

xiv

1: INTRODUCTION

It is a scorching hot, summer day in Mexico. You are sitting at the resort pool when hotel staff informs you that the eye of a hurricane is heading straight for your hotel. With insufficient time to evacuate, you are trapped at your hotel and locked in your room, mere feet from the ocean, with no lighting or air conditioning, simply hoping to survive a category five hurricane.

I was personally one of Hurricane Dean’s prey that night. We were confined to our rooms at around 3:00 pm on Monday, August 20, 2007. We had intermittent television prior to losing our power, and we watched CNN to see how close the hurricane was, when it would hit, and how bad it would be. All we knew was that outside our room, the sky was blood red, large palm trees were hurling past our window, and large waves were crashing on our doorstep.

As we sat in the dark, fearing for our lives, wondering if we would stand a chance when the huge waves flooded our ground-floor room, a thought was triggered regarding the relationship between hurricanes and crime. Though a terrifying ordeal, some would suggest that at least we were warned; this is not so in aspects of life such as crime where, more often than not, there is no warning that something terrible is about to occur! Is it true that crime strikes when you least expect it? Is it true we never believe we could fall victim to a crime? Or is crime completely unexpected, its victims picked at random?

Crime is not random. Some elements of crime are very predictable, while others are slightly more difficult to predict, but still create rather specific patterns that lead to predictability. Such variability in crime prediction leads us to question whether crime is not similar to natural disasters like hurricanes or earthquakes.

For example, if a hurricane is travelling at a specific speed and the wind is increasing in a certain direction, we should be able to calculate the probability that it will hit location ‘A’ and the approximate time it will reach this location.

However, if the hurricane is headed north and runs into an island, the hurricane’s velocity and the direction in which it is travelling can change completely. This is not so different from crime. For example, if a certain location in the downtown area of a city is notorious for its higher than normal crime rates, the city, in an attempt to counteract this problem, may build a police station in the area and then tear down all the old buildings, replacing them with expensive high-rises and shopping malls. Crime might then possibly disperse. The offenders could be displaced to the next similarly disadvantaged neighbourhood, and crime there might then increase; this scenario is similar to a hurricane’s path being deflected by an island.

Many critics argue, however, that crime cannot be predicted owing to the complexity of human behaviour, and that prediction may actually increase the amount of crime in society (Harcourt, 2007); such critics explicitly posit that past behaviour should not be used to predict future criminal acts (Gibbs Van

Brunschot & Kennedy, 2008). Though this argument seems reasonable on its face (face validity), this thesis demonstrates that even with complex human

behaviour, crime patterns are surprisingly foreseeable. Specifically, certain elements of human behaviour (e.g., routine activities) can generate predictable patterns within their environment.

Similar to Routine Activity and Crime Pattern theories, the foremost emphasis of Environmental Criminology is directed towards the convergence of setting and opportunity (Rossmo, 2000). The interaction between a person’s physical setting and their behaviour creates varying levels of opportunity to commit crimes (Felson & Clarke, 1998). The existence of this convergence based on these theories lends credence to the spatial analysis of criminal events.

By combining many aggregated individual acts, more general patterns can be rendered visible on a map.

With the creation of aggregate patterns, crime prediction models (i.e., risk models) that utilize techniques similar to those used in hurricane and earthquake modelling should be able to successfully predict aggregate crime patterns. It is also believed that such techniques will better (i.e., more accurately) predict crime locations for offences involving static targets than it will mobile targets, because the positions of the latter are dynamic and more difficult to predict (similar to hurricane prediction methods). Crime prediction should therefore be more accurate when applied to burglaries, given that houses are static structures, rather than assault, as people are generally more mobile than buildings).

This thesis describes a methodological review that used reported assault and break-and-enter crimes in Regina to explore spatial-temporal patterns of crime and then developed and used hazard-risk modelling to improve methods of

predicting future crime concentrations. In order to explore and improve current hazard-risk methodological models in criminology, new software was developed for the task (Crime Risk Assessment Software). The software created a geostatistical risk model of two crime types, assault and break-and-enter

(dynamic and static, respectively), to determine whether geostatistics, specifically

Kriging techniques, could create strong predictive risk surfaces of these crimes.

Geostatistics involve many statistics including Kriging. This thesis explores the use of Kriging in the analysis of crime patterns. Kriging can be used to describe and interpolate from a dataset to areas where little or no information is available (known as prediction or forecasting). It is commonly applied in fields such as geography, oceanography, epidemiology, forestry, and meteorology

(Myers, 2009).

As Kerry noted in 2010, geostatistics such as Kriging have rarely been applied to crime data; only two studies have applied it in this fashion (see

Camara et al., 2004; and Kerry et al., 2010). However, the current research not only applies a geostatistical model (e.g., Kriging) to determine whether it might sucessfully predict criminal behaviour, it also determined whether such models would more accurately predict static crime than dynamic crime, owing to the mobility factor.

Meeting the goals just described not only adds to the growing body of spatial literature, it will also help researchers create more dynamic and predictive crime analysis techniques, by utilizing more accurate measures that can then be used to analyze a wider range of static and dynamic crimes.

Chapter 2 presents an overview of risk and hazard modelling, first by describing such modelling and how it can most effectively be applied, and second, by providing an overview of research in the realm of public safety.

The theoretical framework from Environmental Criminology is then reviewed in order to ground the use of spatial and geostatistical analysis in the field of criminology. As mentioned, this study was not a test of theory, rather a methodological review and use of a new modelling method. Overviews presented in this dissertation of common theories such as Crime Pattern Theory and

Routine Activity theory are provided in order to ground the use of spatial and geo-statistical analysis within the field of criminology. A case study provides the means for an overview of both the available research regarding static and dynamic crimes and of the methods and results used to test the data and build the risk models. It concludes with a discussion of the potential impact that the results obtained may have on current and future research.

2: RISK & HAZARD MODELLING

The concept of creating spatial risk and hazard models is relatively new to

criminology; the use of such geostatistical models, in particular Kriging, is

considered extremely rare, though it is beginning to gain more attention (see

Kerry et al., 2010). Because using such concepts is so new to criminology, this

chapter first explains what risk and hazard modelling is, how such models were

applied in this research, and the justification for applying them to crime data. The

focus of this chapter is to discuss how such risk and hazard models enhance

public safety, but before we can explore their utility in that realm, they must first

be defined further, as they are often used interchangeably.

2.1 Defining Risk, Hazard, and Vulnerability

The term “risk” did not ultimately take hold until the sixteenth and

seventeenth centuries, when it was used by Western explorers to refer to sailing a boat into uncharted waters (Veritas, 2008). The term currently implies a level of uncertainty (Wilson & Shlyakhter, 1997) similar to the trepidation that arises from

literally or figuratively sailing into uncharted waters. Risk can be seen as the

probability of an adverse outcome (Tobin & Montz, 1997) or the chance that a

hazard will actually cause harm to someone (NOAA, 2004). As Wilson and

Shlyakhter point out, “if there exists an uncertainty whether a hazard exists, there

remains a probability that it does and therefore a risk” (1997, 1).

A typical hazard identifies anything that is capable of causing harm (e.g.,

oil on the street or a banana peel on the floor), whereas a natural hazard more

specifically represents the potential interaction between humans and extreme

natural events (Tobin & Montz, 1997). Natural hazards are also often referred to

as natural disasters, though the key distinction is that the natural hazard is only a

potential event, while the disaster is the hazard’s actual occurrence (Tobin &

Montz, 1997).

The importance of clarifying the concepts of risk areas and vulnerability

lies in their common usage in probability calculations of a hazard. Risk areas

identify the geographic locations represented cartographically, meaning those

areas more likely to be affected by a hazard (NOAA, 2004). People can live

within a risk area and be exposed to risk from hazards, but they may not

necessarily be vulnerable to the hazard impacts (NOAA, 2004). This is why the

term vulnerability should be clarified.

Vulnerability is also often incorrectly used synonymously with the term risk. Where risk is the probability of an adverse effect, vulnerability is defined as the potential for loss (Tobin & Montz, 1997). As the NOAA Coastal Services

Center points out, “vulnerability of the people and resources within the risk areas

is a function of their individual susceptibility to the hazard impacts” (2004).1

Therefore, as mentioned above, being located in a risk area does not necessarily make one vulnerable. For example, let us assume that a hazardous chemical

1 NOAA. (2004). Risk and Vulnerability Assessment Steps: Hazards Analysis Extended Discussion. Coastal Services Centre. Retrieved, 2005, from the World Wide Web: http://www.csc.noaa.gov/rvat/hazardEdd.html.

was spilt within the defined risk area where an individual was positioned. Then let

us further assume that, within this area, the potentially at-risk individual was located uphill and across the street from where the emergency response team worked to clean up the spill. The individual’s vulnerability would decline in direct proportion to the decreasing likelihood that he or she would be harmed by the hazard.

Within the field of criminology, the term risk is most often associated with recidivism, or more specifically, the prediction techniques used to determine the likelihood of an offender committing another crime.2 For example, Klieiman and

Kilmer studied risk by analyzing the amount of punishment that must be applied

to an offender before they would be considered to be at risk to reoffend (2009),

and Belfrage et al., (2004) utilized qualified risk assessments to determine

whether violence toward correctional security personnel could be minimized.

Campbell, et al., (2009) conducted a meta-analysis of risk assessment

instruments and methods, where they found hundreds of risk studies could be

said to have been conducted in the field of criminology, given that their meta-

analysis included analysis of 88 studies with more than 70 different risk

measures.

From the perspectives of Environmental Criminology and Routine Activity,

risk can be determined by the convergence of a motivated offender, a suitable

target, and the absence of a capable guardian at a particular space and time

(Zhang et al., 2007). Daily routines or activities affect the likelihood of that

2 Recidivism can be defined as the “repetition of criminal behaviour by an offender previously convicted and punished for an offence” (Drislane & Parkinson, 2005, p. 118).

convergence, therefore influencing the risk of being victimized (Zhang et al.,

2007).

Owing to the inherent complexity of assessing real and perceived risk, it is

difficult to predict individual criminal events. However, within each of these

concepts, variations of risk surfaces or hazard models have been developed. The

following section presents an overview of the application of hazard and risk

models and provides specific examples of how such techniques are applied to

the area of public safety.

2.2 Risk & Hazard Model Applications

From an Environmental Criminology approach, the convergence of the

certain factors such as environment, motivation and opportunity factors can

increase the “risk” of a crime occurring (see Brantingham & Brantingham, 1993;

Felson & Clarke, 1998). It is believed that larger aggregate patterning is created

through the convergence of these factors that supports the use of risk modelling techniques from other fields, such as health and geography. Ideally, because this spatial convergence creates aggregate patterns, the use of risk modelling techniques should help predict the risk of criminal behaviour occurring.

The most basic level of risk and hazard calculations can be expressed as follows:

Equation 1 Risk Calculation (Tobin & Montz, 1997)

Where:

= Probability (the likelihood of the occurrence)

= Risk (the probability of an adverse effect)

= Exposure (the size and characteristics of the at-risk population)

= Vulnerability (the potential for loss)

= Response (the extent to which mitigation measures are in place)

Risk surfaces and hazard models dominate in areas of public safety, including the health and environmental fields (see Jarup, 2004; Kelsall & Wakefield, 2002;

Maantay, 2002; Richardson et al., 2004), but only lately has such modelling been considered useful in the field of criminology (see Andresen, 2006; Ceccato &

Haining, 2005). In the past, risk models in many fields, specifically criminology, were constructed using mathematical calculations in a two- or three-dimensional analysis without accounting for spatial variables. More recently, however, researchers have started to build more robust and predictive models with multiple methods of analysis that not only incorporate risk calculations but also add spatial depiction and interpretation (see Grubesic, 2006; Harada & Shimada,

2006). For example, Kelsall and Wakefield (2002) utilized geostatistical models to predict the spatial variation of the incidence of disease and mortality across

geographic regions, while Juliana Maantay (2002) demonstrated how mapping

risk could be used to determine disease rates in specific populations.

Risk models in particular predict losses through probability calculations

and/or geographic analysis (Wilson & Shlyakhter, 1997). Risk assessments in

law enforcement have typically been negatively associated with the prediction of

recidivism. More recently, however, risk models have expanded upon these

mathematical calculations by adding spatial methods to build more robust and

predictive models utilizing multiple methods of analysis (see Andresen, 2006;

Barthe & Stitt, 2007; Ceccato & Haining, 2005; Zhang, 2007). As Wilson and

Shlyakhter (1997) explain, “quantitative analysis of uncertainty and variability is

receiving growing acceptance in risk assessment” (1).

To provide an overview of how hazard and risk modelling is applied to

public safety, it is important to discuss its breakdown into mathematic and

cartographic3 models, as they represent two different approaches to risk analysis. Mathematic models are variations of probability calculations, and they have a longer history in risk or hazard analysis than do cartographic models.

Despite the elementary form in which risk is calculated in Equation 1, it

none-the-less depicts the foundation for risk- and hazard-based conceptual models. More precise and accurate forms of analysis can be broken down into two models: mathematical calculation models and combined cartographic/mathematic models. Purely mathematical models are simply a

3 Cartographic models use multiple geographic methods to visually depict data in a design on a map (Steinberg & Steinberg, 2006).

probability calculation within which geographic or spatially based data is not accounted for; the statistics are simply based on the likelihood of an event occurring. Monte Carlo simulations are a form of mathematical techniques used to quantitatively assess risk analysis that:

“allows analysts to assign probability distributions to all uncertain

components of a mathematical model of the problem and then,

through random sampling of these distributions, determines the

distribution of all potential outcomes that could occur under these

uncertainties” (Vose, 1997, 1)

It is important to note that the benefit of using Monte Carlo simulations is that they encompass a wide range of techniques to mathematically describe the impact of uncertainties (Vose, 1997).

Spatial analysis, particularly prediction, is beginning to be more widely used in criminology. Despite its drawbacks (see Wilson & Shlyakhter, 1997), notably the Modifiable Areal Unit Boundary (MAUB) problem that is discussed in

Chapter 5, Maantay (2002) effectively demonstrates that the benefits of spatial analysis and prediction still largely outweigh the negatives. However, spatial prediction does not neglect the application of statistics. In order to create a solid geographical predictive model, probabilities must be calculated. The benefit to spatial predictive modelling is the ability to depict areal data (i.e., geographical/ environmental data) and overlay it with hazard effects in order to produce a predictive illustration of both local and global risk.

When we examine public safety policy, we note that all potential hazards contain at least some environmental factors, including climate, toxic substances, health, pipelines, food contamination, spread of disease, crime, etc. These attributes have a solid geographical component that can play a significant role in the analysis of risk and hazards by providing a more accurate assessment of potential exposure to a hazard.

As an example, Juliana Maantay (2002), based on research conducted in the area of disease mapping, argues that incorporating geographic and temporal analysis, rather than only statistical modelling, might shed more light on previously unrecognized patterns; this, in turn, will help provide more answers and/or future research directions. Maantay also notes that geographic analysis can enhance investigations by modelling health outcomes with aggregated exposure data at the set boundary level (such as a census tract or health district) in order to model possible exposure related to disease incidence data (2002).

Another example is analyzing the risks of air pollution emissions from hazardous facilities. In these instances, mathematical models are executed externally to GIS, where the spatial patterns of the average concentration of these pollutants emitted into the air can be estimated (Maantay, 2002). A further benefit derived from using such models is that plume buffers4 can be overlaid on the census data to help determine the characteristics of the exposed populations

(Maantay, 2002). Such information is used to change policies on emission

4 A buffer is a circular outline or representative distance overlaid around a point location or geographic feature of interest (Steinberg & Steinberg, 2006).

standards to reduce harm to both the environment and to the population living near hazardous facilities.

Risk surfaces have also successfully depicted the distribution of risk factors spatially in the public health field (Bertollini & Martuzzi, 1990). As Lars

Jarup (2004) explains, spatial analysis helps identify disease clusters and health patterns, as well as defining and monitoring epidemics and demonstrating changes in disease patterns over time. For example, such analysis has affected decision-making criteria as well as the choice of preventions and interventions used to target and avoid risk factors (Bertollini & Martuzzi, 1990). As Jarup

(2004) pointed out, one of the most compelling advantages to using risk and hazard models is that the possibility of modelling exposure geographically positively affects how individual exposure is estimated (i.e., without time- consuming and costly measurements).

The Kyoto Protocol5 offers another promising example of how hazard models might be used. Climate change is an on-going concern, not only in

Canada but throughout the world; even a small degree of change in temperature can have a significant impact on the environment (Northern Territory

Government, 2007). According to William Leiss (2002), risk in this scenario is characterized by emissions of greenhouse gases (GHGs). We can diminish those emissions substantially by reducing our usage of fossil fuels (Leiss, 2002).

The problem lies in determining at what level of reduced fossil fuel usage our

5 The Kyoto Protocol was made official on 16 February 2005 (Foundation, 2008). Specifically, it is a “binding international agreement that sets targets to reduce the greenhouse gas emissions that cause climate change” (Foundation, 2008, p. 1).

industrialized society can continue to function adequately, now and/or in the future–determining that balance is extremely difficult from a policy perspective.

On the one hand, scientists warn that not reducing GHG emissions will lead to such extreme climate changes that we cannot afford to take that risk

(Leiss, 2002), thus from the policy perspective, if the emissions levels are too high, the result will bring about significant harm. However, completely eliminating the use of fossil fuels by factories, cars, trains, boats, and planes, to mention only a few examples, would bring society as we know it to a virtual halt. Given the need to balance use against harm, it is important for risk analysis to predict the most likely scenario, such that policy-makers are well informed prior to implementing or changing policy.

Kyoto was a large-scale agreement entered into by 180 countries with a commitment to reduce their individual GHG levels by the year 2012 (Environment

Canada, 2002). This example demonstrates how difficult it is to determine the critical balance between losses and gains; the public is at risk from climate change effects if Kyoto is not implemented, but public safety could also be compromised if we stop using fossil fuels completely.

Within the field of criminology, multiple methods of risk analysis have been used spatially to create a risk model at a somewhat functional level (see Liu &

Brown, 2003; Camara et al., 2004; McLafferty et al., 2000), though not to the same extent as the examples discussed above. For example, Chris Brunsdon and Jon Corcoran (2006) used what are known as circular statistics to analyze time patterns inherent in the incidence of crime . They included a combination of

Kernel Density estimations and compared patterns to Monte Carlo simulations to

test the overall temporal distributions of crime incidents, discussing how these

techniques can be adapted for varying temporal data. Yutaka Harada and

Takahito Shimada (2006) also used Kernel Density techniques to estimate the

density of crime location concentrations in specific areas in Japan. After

analyzing 11,096 points of residential burglary incidents, they provided guidelines

for cell size and bandwidth to address the poor precision of geocoding issues

(Harada & Shimada, 2006).

The majority of practical applications and uses of risk and hazard models

seen throughout the literature are from the public safety arena (see Jarup, 2004;

Kelsall & Wakefield, 2002; Maantay, 2002; Richardson et al., 2004). This is because geographic information systems have historically been used primarily in the fields of geography, the health industry, and the environment. More recently, these methods are being increasingly used in applications commonly associated with law enforcement (see Brunsdon & Corcoran, 2006; Grubesic, 2006; Harada

& Shimada, 2006). The purpose of the following section is to explore specific examples of hazard and risk model research that was conducted using

techniques similar to those previously discussed. Reviewing research in other

areas of risk and hazard modelling facilitates comprehension of the concepts and

framework used to develop the model for this thesis.

2.3 Examples of Risk and Hazard Models in Public Safety

As previously mentioned, spatial analysis techniques are being used in

many areas. Mapping forestry events has played a particularly large role in

spatial analysis research. For example, Meentemeyer et al. (2004) used spatial

analysis to study California forests in order to analyze the risk of sudden oak death, an emerging disease reaching epidemic levels; it provided a solid example of the utilization of spatial analysis in risk mapping. Many comparable studies

have also been conducted using similar techniques in other parts of the world

(see Lalibert E. et al., 2008; Liu & Brown, 2003; Tang & Baldocchi, 2005).

In the sudden oak death study, five predictor variables were mapped using

GIS to generate a model illustrating the spread of the disease based on

variations in environmental conditions (Meentemeyer et al., 2004). In this model,

the spread of the risk was mapped by averaging the predicted risk for each

reproductive month (December to May) and then creating a risk index for these

variables (Meentemeyer et al., 2004). The risk index was then mapped by

creating a polygon map of each county in California, associating the risk index to

a polygon boundary. Though the results appear dramatic, it was actually a rather

simple way to use cartography to depict risk. This polygon technique was similar

to exploratory methods used in this study to assess the aggregated crime data at

a census tract level (see Chapter 4).

Another example of risk analysis using a similar technique addresses

areas affected by air pollution. Given that pollution is a significant public safety

concern and will be for many years to come, modelling techniques have been

developed in an attempt to visually represent the risk of exposure to society. In a

study conducted by Lejano, Piazza, and Huston (2002), spatial illustration of data

was used (polygon depictions) to illustrate how residents in different areas of Los

Angeles were exposed to potentially cancer-related levels of pollution. Multiplying

the concentrations of exposure by the cancer-related factors created a cumulative cancer risk value for each census tract in the region. This cumulative

cancer risk, similar to the previous study, was then associated with its

corresponding census tract (polygon) to depict a visual illustration of risk across

the study area. Unlike the current study, they produced a visual depiction of risk

associated with a polygon boundary rather than a smoothed risk surface.

Interestingly, they also correlated their predictions of cancer with

demographic variables and found that cancer risks were demonstrably

associated closely with lower income and minority communities (Lejano et al.,

2002). However, as previous studies explained, this is not so much a causal link

as it is a correlation based primarily on location (Lejano et al., 2002). As Maantay

(2002) pointed out, mapping environmental injustices such as this one is not straightforward. The difficulties inherent to producing such maps leave them open to a wide range of interpretation and second-guessing (Maantay, 2002).

Despite the fact that pollution has higher risk factors and concentrations in specific areas, without examining these areas at a local level, predictive factors

(such as income or minority status) that may appear significant might, in fact, be due simply to the development or planning of the city. Regardless, according to

Maantay (2002), mapping should not be used as a solution to prediction; it should instead be used in combination with multiple approaches to analyze the phenomenon in question. A solid statistical model utilizing a variety of spatial

analysis and statistical approaches can create stronger outcomes, rather than

relying solely on a cartographic representation of data.

Spatial epidemiology is another area in public safety that describes and

analyzes geographic variations in disease, utilizing demographic, environmental,

genetic, socioeconomic, and other risk factors in model formulations (Elliot &

Wartenberg, 2004). Many of the methods employed in spatial epidemiological

studies have also been applied to crime analysis in the law enforcement field, as

both address, or are affected by, the element of human complexity. The

application of the type of spatial techniques used in spatial epidemiology for

predicting health and disease issues enhances current spatial techniques used in

the analysis of risk and hazard models (Blanco et al., 2004; Cocking & Martin,

2004; Elliot & Wartenberg, 2004; Jarup, 2004; Kelsall & Wakefield, 2002; Lawson

& Clark, 2002; Maantay, 2002; Richardson et al., 2004).

The validity of spatial analysis involving human behaviour has long been

debated, as it assumes some form of predictability, and not all researchers agree

that behaviour is predictable or patterned (Harcourt, 2007). Human beings are

also rather dynamic and not static over time. These dynamic factors make the

measurement of certain types of criminal events even more difficult as they are

mobile and factors can change over time. For example, geographic methods are

available to measure subjects as varied as air pollution and bear habitats, but

human behaviour is not always easily predictable. Numerous complex factors

may account for one store being robbed five times more than the store across

the street (see Brantingham & Brantingham, 1984; Brantingham & Brantingham,

1995a; Brantingham & Brantingham, 1993; Clarke & Felson, 1993; and Felson &

Clarke, 1998). It might be the parking, the ease of entrance, the type of road

network leading toward each store, or the type of product sold. It could even be

the store’s owner, security levels, etc. The crime might depend on the daily activity pattern and the exact pattern of a potential offender. The potential offender has to be near a good target at a time when the wish to commit a crime is high. Other concerns when analyzing criminal events such as murder, for example, can involve situations where the initial crime may not even occur at the same location as the body recovery site. A criminal event at multiple locations adds even more complexity to the analysis of predictive factors.

Spatial epidemiology studies analyze many factors that are, however, more consistent with criminal activity. According to Elliot and Wartenberg (2004), spatial epidemiological studies focus on demographic, environmental, genetic, socioeconomic, and risk factors pertaining to disease. Criminal justice researchers examine a similar list of predictive factors including demographic, environmental, genetic, socioeconomic, and risk in their search for crime patterns or occurrences.

The three types of spatial epidemiologic inquiry include disease mapping, geographic correlation studies, and cluster analysis (Elliot & Wartenberg, 2004).

These three forms of analysis play a crucial role in law enforcement from crime mapping, to criminal event correlation studies, to crime hot spot and cluster analysis studies. However, the same problems evident in spatial epidemiology also occur in crime mapping. Griffith (2008), for example, suggests the current

stumbling block for both fields includes the lack of small area data and/or a lack of access to data and polygon features. It is difficult to speculate at global levels of analysis without detailed situational data.

The last model examined here was developed by Chen et al. (2004). The catastrophe loss estimation6 is a more detailed model that illustrates the use of geographic analysis in examining two natural hazards: earthquakes and hailstorms. Their study raised many intriguing methodological concerns regarding the specified areal unit (e.g., census tract or health district); however these boundary issues will be discussed in more detail in Chapter 5. For now, it is useful to note that the study itself focussed on catastrophic loss modelling for natural hazards comprised of four stages of analysis: hazard, exposure, vulnerability, and risk (Chen et al., 2004). Each stage of the analysis utilizes a different statistical or cartographical technique.

In this model, hazard analysis is considered the quantification of the physical characteristics of a hazard, while the exposure analysis maps and identifies the underlying elements at risk (Chen et al., 2004), and vulnerability analysis assesses the degree of susceptibility when elements at risk are exposed to the hazard (Chen et al., 2004). Risk analysis combines these first three factors

– hazard, exposure, and vulnerability – in order to determine the resulting losses

(Chen et al., 2004). The diagram below is a visual illustration of the four components of this catastrophe loss model:

6 Catastrophe loss estimation modelling is a concept created by Chen et al. (2004) which illustrated a technique comprised of four types of risk prediction tools used to estimate the amount of loss that would result should a particular hazard occur.

Figure 1 Catastrophe Loss Model

In Figure 1, it is evident that risk is a function of the three components, expressed as risk = f (hazard, exposure, vulnerability) (Chen et al., 2004). The next stage of the model was to define the area at risk. However, a mapping assumption states that a value at risk should be uniformly distributed across each unit, and such distribution is highly unlikely, whether the unit be census tract or boundary (Chen et al., 2004). Analysis is also so dependent on the size of the unit chosen that changes in the boundary size may very well impact the results of the analysis

(this has been termed the modifiable areal unit boundary problem [MAUB]). This factor is also discussed in more detail in Chapter 5, but here it is important to note that choosing the unit of analysis from which to aggregate the data could have a significant impact on the results. Therefore, it was important to choose the

most appropriate measurement areas when multiple methods of analysis are

planned in order to avoid MAUB discrepancies.

In this catastrophe loss estimation study, the authors, in their attempt to

account for the MAUB issues that would impact their study, utilized a new modelling technique called “dasymetric mapping” and “areal interpolation” (Chen et al, 2004). To illustrate this technique’s utility, consider conducting a study measuring the socioeconomic data from census zones for residents. Each census tract overlays the data uniformly across the tract, but residents are not distributed uniformly, thus rendering the analysis inaccurate. Dasymetric mapping transforms the example of socioeconomic data from census tracts to residential areas according to areal interpolation rules (see Figure 2 below)

(Chen et al., 2004), thereby potentially resolving this imbalance.

Figure 2 Dasymetric Mapping

The public sector uses this form of risk or hazard analysis much more frequently

than it has in the past. A discussed later, despite the differences in techniques

demonstrated in this section, all of these models support the need to borrow techniques from these studies to build more robust models of crime analysis.

2.4 Case Application of Geostatistics

A key point from the research discussed above is the need to rely on multiple methods of analysis when building a more accurate predictive model. In this study, the risk model discussed further in Chapter 4 was built using knowledge and concepts associated with risk and hazard models from the studies discussed above combined with geostatistical techniques used in geography. Geostatistical models are a branch of statistics used to describe and interpolate the data from a dataset to areas where little or no information is available (known as prediction or forecasting).

Currently, criminologists and geographers tend to use a method called kernel density or kernel smoothing to analyze crime data (see Chainey &

Ratcliffe, 2005; Rengert, et al., 2005; Groff & La Vigne, 2001). Similar to Monte

Carlo modelling, kernel density estimates the probability density function (f) of a distribution from which the sample {xi} has been observed (Brunsdon, 1995).

However, it differs from the Monte Carlo method in that the probability density function is conducted spatially by centering the probability distribution function, k , around each observed point and then taking the average value of all of the points (Brunsdon, 1995). Statistically, this estimation is expressed as:

Equation 2 Kernel Density Estimation (Brunsdon, 1995, 878)

Where:

= the number of observations in the sample

= the radius of the kernel estimation, and where

is usually considered to be Gaussian with a mean of 0 and a variance of 1

The problem with this approach is that large ( ) values in the radius will cause ( ) to also have a large variance (Brunsdon, 1995). Phaedon Kyriakidis (2004) believes that it can be seen as a variant of the geostatistical approach, but also states that it does not yield solid predictions based on inconsistent modelling of area-to-area and area-to-point covariance.

Due to these inconsistent models, Brunsdon created an adaptive kernel estimation technique that allows “the value of ( ) to range between different regions of the sample space” (Brunsdon, 1995, 879–80). The equation then becomes:

Equation 3 Adaptive Kernel Density Estimation (Brunsdon, 1995, 880)

Where:

hi varies with xi

This adaptive kernel density estimation accommodates local variations in point

pattern characteristics by adapting the parameters that control the surface

estimation adjusted over geographic space (Brunsdon, 1995).

The geostatistical model developed for this study was based on a variation of the traditional Kriging methods (the details of the specific variations applied to this method is discussed in depth in Chapter 4). Kriging is a method used to smooth or interpolate spatial data (Diggle et al., 1998). It was created as a spatial

prediction method designed to predict an areal value with available areal data of

the same or different variables (Kyriakidis, 2004). In the past, it has been

employed by such researchers as Kelsall and Wakefield (2002) to estimate the

latent risk surface of disease incidents (Kyriakidis, 2004). Kriging is a technique

that interpolates the value at a location through a weighted summation of values

at surrounding points (Okanbe Lab, 2002). This estimation function can be

expressed as:

Equation 4 Kriging Estimator Function (Diggle et al., 1998, 299)

Where:

Zˆ( ) = the measured value at the ith location si

th λi = an unknown weight for the measured value at the i location

= the prediction location s0

N = the number of measured values

Kelsall and Wakefield (2002) also used Kriging, but they used it in a lognormal7 setting (Kyriakidis, 2004). Though this method appeared solid at the time, it has been criticized for its incoherent predictions owing to “the nonlinearity of the logarithmic transformation involved in lognormal Kriging” (Kyriakidis, 2004). As diverse forms of Kriging methods continue to be employed by researchers, variations of these techniques continue to be created and tested. Chapter 4 depicts the details surrounding the use of Kriging in this study specifically.

In the past, Kriging has been used in many different fields such as geography, oceanography, epidemiology, forestry etc. Kelsall and Wakefield

(2002) utilized it to estimate the latent risk surface of disease incidents

(Kyriakidis, 2004). Baalousha (2010) combined multiple methods of vulnerability mapping, including Kriging, to identify areas of high pollution potential and their

7 A lognormal distribution is where the log of a variable is normally distributed.

spatial distribution. Goovaerts et al. (2008) used Kriging to create a geostatistical

model analyzing the spatial distribution of soil dioxins near incinerators.

Unfortunately, due to the relatively new application of geostatistics in

criminology, the use oftechniques such asKriging is extremely deficient. To date,

only two studies have been found. The first was conducted by Camara et al. in

2004, but it is not particularly helpful as it used relatively ‘rare’ homicide events that had extremely minimal number of points. However, Kerry et al. (2010) recently published a study that used Kriging techniques to analyze car thefts in the Baltic States. They found the use of Kriging improved the interpretation and understanding of crime patterns as compared to the more ‘typical’ techniques often used (Kerry, 2010).

Despite this lack of research application to criminology, model building using geostatistics such as Kriging show promise when applied to crime data

(Kerry et al., 2010). The current research uses a combination of the methods above to construct a robust predictive model (a more detailed description of this process is provided in Chapter 4). However, prior to discussing the current case study, it is important to discuss the theoretical foundations supporting crime mapping. Even though this study is rooted in probability theory that focuses on geostatistics, specifically Kriging, justification to conduct spatial analysis for this study was grounded in Environmental Criminological theory. The following chapter provides a brief overview of the Geography of Crime, focussing specifically on the theoretical foundations that support the need to conduct risk analysis in criminology.

3: THEORETICAL FOUNDATIONS FOR SPATIAL ANALYSIS

The Environmental Criminology perspective posits that crime can best be

discerned by considering potential offenders and targets alongside their proximal

and distal surroundings (Brantingham & Brantingham, 1997). Comprehending the

phenomenon of crime is an on-going process, not only within criminology but

across multiple disciplines (Guarino-Ghezzi & Trevino, 2005). Regardless of one’s definition or perception of crime, the ultimate goal of every justice professional is to reduce the propensity for criminal activity to occur, though there is no consensus regarding the most effective means by which to accomplish this.

The objective of this thesis was to explore spatial-temporal patterns of crime and to develop and use hazard-risk modelling to improve methods for predicting future crime concentrations. Specifically, new software was created

(Crime Risk Assessment Software) in order to explore and improve current hazard-risk models in criminology. The software was used to create a geostatistical risk model of two crime types, assault and break-and-enter

(dynamic and static, respectively), to determine whether geostatistics, specifically

Kriging techniques, could create strong predictive risk surfaces of these crimes.

The purpose of the thesis was not to test theory. Rather, it was considered an

exploration of methods used to predict patterns of crime grounded in theory.

Nonetheless, when analyzing concepts and methods in criminology, it is useful to

explain the theoretical contributions to the study of the Geography of Crime to provide substantive understanding of the analysis of people, crime, and space.

The following chapter offers a brief overview of theoretical contributions to the Geography of Crime, highlighting the general progression from theory to application. Specifically, it reviews several of the key theoretical contributions to this field, concentrating particularly upon crime patterns. The next section examines environmental theory and outlines the differences in micro, meso, and macro explanatory levels.

3.1 Levels of Environmental Theory – Micro, Meso and Macro

From within an Environmental Criminology perspective, Brantingham and

Brantingham (1991) proposed three prospective levels for the analysis of crime: micro, meso, and macro. Macro approaches involve large scale analyses that compare the distribution of criminal activity between cities, states/provinces, or countries; meso level explanations of crime analyses are directed toward studying crime within the boundaries of a city or metropolis; whereas micro levels examine the smallest dimension of crime, including site-specific locations, building types, landscaping, lighting, security, etc. (Brantingham & Brantingham,

1991).

In regard to these perspectives, it is believed that studies involving early attempts to understand the relationship between crime and place tend to take a more macro approach, looking at aggregated information such as regions, states, cities, etc., instead of using a micro approach to examine the actual context of

the site itself (Eck & Weisburd, 1995). In criminology specifically, former theories have been criticized for being “far too limited, focussing primarily on conceptually constrained origins of the desire or willingness to commit crimes rather than on complex patterns in crime” (Brantingham & Brantingham, 1993). Theories related to the microanalysis of crime have progressed a great deal from the time when

these preliminary efforts were popular.

Since the early 1900s, the integration of macro, meso, and micro

explanations for crime and criminality across multiple disciplines (as opposed to

a single explanation) has grown. Studies of the environment or of the urban

impact on crime have also expanded to include increased meso- and micro-level

analysis. As John Eck and David Weisburd pointed out in 1995, “such studies

began with efforts to identify the relationship between specific aspects of urban

design (Jeffery, 1971) or urban architecture (Newman, 1972) and crime, but

broadened to take into account a much larger set of characteristics of physical

space and criminal opportunity” (Eck & Weisburd,1995, 3).

In the context of this thesis, it is important to understand the connection

between crime and the environment from within all three approaches,

specifically, how crime can be predicted more accurately based on peoples’

routine activities and patterns (Brantingham & Brantingham, 1997). This chapter

explores the Geography of Crime and Environmental Criminology, outlining

common theories used to determine how targets or victims are selected (e.g.,

opportunity and lack of guardianship), why crime seems to be concentrated in

certain areas (i.e., hot spots), and how criminal patterns are created.

3.2 Geography of Crime

The Geography of Crime can be seen as a way of analyzing spatial patterns produced through the interactions of society, space, and crime. Some of the earliest roots of examining criminal behaviour patterns can be seen in works by Quetelet and Guerry from the mid-1800s; they produced the first crime maps displaying the rates of crime by province in France (Wortley & Mazerolle, 2008).

Many theories have been developed regarding the concepts of crime analysis that look not only at the specific Geography of Crime, but also of everything from behavioural to environmental implications. One of the more encompassing ways to think about environment and crime is to examine works from within the field of

Environmental Criminology.

Environmental Criminology analyzes human interaction and criminal events using the law and the environment in addition to economic and social factors (Brantingham & Brantingham, 1997). Environmental Criminology theories provide a range of explanations that draw support from multiple disciplines.

Specifically, crime is explored as an event that can be understood by jointly considering potential offenders and their proximal and distal surroundings

(Brantingham & Brantingham, 1997).

Environmental Criminology is a novel concept for some, though many theorists explained crime decades ago using concepts involving patterns and environment that provided the foundation for our current comprehension. For example some of the earliest foundations of Environmental Criminology can be

attributed to the work of human ecologists dating as far back as the early-to-mid-

1800s.

Some of the earliest influences upon our current understanding of criminal behaviour can be traced back to early Chicago School theories and the evolution of human ecology. Human ecology involves three main themes: plant and animal, geography, and the spatial distribution of social phenomena

(Theodorson, 1982), each of which contribute to environmental theories of crime.

Some of the earliest works were based on Darwin and his followers, owing to their focus on plant and animal ecology (Theodorson, 1982). Though one would not typically attribute criminal theories to Darwin, he did study the interactions of living organisms (i.e., plants and animals), describing that interaction as the “web of life” (Park, 1936).

This web of life specifically illustrates how all living organisms, whether plants or animals, are bound together in an interlinked and interdependent system (Park, 1936). Such a system is not dissimilar to offenders’ interactions within their environments and with the people they know.

Darwin’s observations depicted interactions based on the convergence of animals and plants in their natural habitat (Park, 1936). He is quoted as saying,

“the active principle in the ordering and regulating of life within the realm of animate nature is … the struggle for existence” (Park, 1936, 2). Such a “struggle for existence in human groups’ social organization accommodates itself to the spatial and sustenance relationships existing among the occupants of any geographical area” (McKenzie, 1926, 141). That interrelation and

interdependence are more readily observed within one’s common habitat than

they might be elsewhere (Park, 1936).

The impact of ecological theories on urban features of Environmental

Criminology can be seen in the underlying interactions of humans with space.

Specifically, human society can be categorized into biotic and cultural levels; the biotic level accounts for the unconscious adjustments humans make in the struggle for existence (subsocial), whereas the cultural level is based on communication and consensus (Park, 1982). Park concludes that “the struggle for existence, based on competitive cooperation and resulting in the organization of the biotic level of society, also determines the spatial distribution of persons.

The spatial distribution is therefore seen as reflecting the organization of the biotic level of society” (1936, 3).

Drawing upon this concept of the struggle for existence, many studies and theories evolved from human ecology toward sociological theories. In particular,

Robert Park and Ernest W. Burgess introduced the terminology of “human ecology” in 1921 that represented the convergence of “the basic theoretical scheme of plant and animal ecology to the study of human communities”

(Theodorson, 1982, 3). Specifically, they devised the concentric-circle or

concentric-zone theory in a publication called The City (Park et al., 1925).

Though this theory is not currently supported, it was widely accepted for a significant period of time. The theory essentially relied upon ecology and social disorganization in order to produce a conception of a city as a series of concentric circles, or zones, that radiate outward from the central business

district. Burgess emphasized the utility of the central business district and the variation the surrounding areas based on their distances from, and influence on the central business district (Theodorson, 1982).

The concept of the concentric zones of city growth demonstrated how human behaviour could be spatially replicated. Such spatial replication illustrated how crime increased in certain areas owing to the physical and social areas being less defined, a factor, which resulted in higher proportions of new immigrant populations, higher divorce rates, and housing that was generally not well maintained (Winterdyk, 2006). This transitional zone is sociologically regarded as a highly disorganized area. The concentric zones broken down into types of dwelling areas and districts.

Though successful then, the construction of a city and its social dynamics was transformed over time. More vehicles were introduced, causing changes in traffic and walking patterns. Distance to and from work was reduced as transportation became less costly and more readily available; consequently, people travelled longer distances (Winterdyk, 2006). In addition, the concept did not include changing landscapes or the gentrification of older property. Thus, the use of the concentric zone theory began to abate.

Despite this overall weakening, it was an excellent demonstration of the possibilities inherent in patterning human behaviour based on a set of characteristics. For example, researchers such as Jacobs (1961) and Jeffery

(1971) borrowed from the concept of altering the human environment stemming from Burgess’s work, translating the idea into crime within a more defined

environment. For example, Jane Jacobs’ The Death and Life of Great American

Cities (1961) suggests that modifying the physical environment can reduce crime, an extremely familiar concept that influenced Jeffery’s work, Crime

Prevention through Environmental Design – CPTED (Jeffery, 1971).

Crime Prevention Through Environmental Design (CPTED) has flourished since the original 1971 Jeffery publication (see, for example, Cozens et al., 2005;

Parnaby, 2007). Interestingly, though, as Patricia and Paul Brantingham (1978) point out, many criminologists have equated CPTED with environmental determinism. The environmental determinism perspective implies the existence of a direct cause-and-effect relationship between human behaviour and the physical environment, a concept that the Brantinghams believe to be clearly untenable (Brantingham & Brantingham,1978). As many would agree, human behaviour and the environment are both extremely complex phenomena. Though the environment plays a role, Jeffery argues that it is “composed simultaneously of physical and social elements; and that people and their environments constantly interact with and impact upon each other (the process of behaviour)”

(Brantingham & Brantingham, 1978, 107).

Such concepts from Jeffery’s work have also played a role in the development of the Brantinghams’ theoretical models of Environmental

Criminology. Environmental Criminology today can be considered a sub-field of criminology. Specifically, it is comprised of several theoretical approaches that explore how the occurrence of crime is influenced by multiple factors such as the urban environment (i.e., backcloth),opportunity, motivation, and guardianship

(Brantingham & Brantingham, 1991). At about the same time that the

Brantinghams were developing their theory using the name Environmental

Criminology, Marcus Felson was developing his Routine Activities Theory

(Cohen & Felson, 1979), and Ronald Clarke was developing his Rational Choice

Theory (Cornish & Clarke, 1986).

3.2.1.1 Routine Activity

Routine Activity Theory is a macro approach with micro-level elements that was developed in 1979 by Lawrence Cohen and Marcus Felson; it was originally an approach to the study of larger trends and patterns (Williams &

McShane, 2008). Based on Amos Hawley’s Theory of Human Ecology in 1950, it

focuses on how crime rates emerge and on the impact that societal technology

and organization has on crime (Felson, 2008). Hawley treated the concept of

crime as a symbiotic relationship between the predator (offender) and its prey

(victim) (Felson & Cohen, 1980).

Routine Activity Theory posits that the potential for any crime to occur is

based on three criteria: a motivated offender, a suitable target, and a lack of

guardianship (Cohen & Felson, 1979). The micro level components of the theory

surround the convergence of a likely offender with a target and the absence of a

guardian (Felson, 2008). As Felson(2008) further points out, a guardian in this

approach does not necessarily mean a police officer or security guard; rather, a

‘capable guardian’ can be anyone whose presence affects the criminal’s decision

to commit an offence . The theory posits that aspects of the larger society or of

the communities that comprise the macro components of this approach may

contribute to the convergence of those three criteria, thus resulting in an increased opportunity for criminal behaviour to occur and making crime the more likely outcome (Felson, 2008).

As Cohen and Felson point out, however, “structural changes in routine activity patterns can influence crime rates by affecting the convergence in space and time” (1979, 589). Several concepts crucial to understanding the analysis of one’s routine activities and how crime sites or targets are selected exist within this framework. These concepts include the offender’s decision-making process and our understanding of the following: backcloth, crime generators and attractors, the offender’s awareness of space, and the specific crime itself. All of these concepts are effectively explained not only by Routine Activities, but also by Rational Choice and Crime Pattern theories, all of which were being developed around the same time in the late 1970s.

3.2.1.2 Crime Pattern Theory

Within the Environmental Criminology perspective, Paul and Patricia

Brantingham, in the late 1970s and the early 1980s, used their model of “offence selection” to create Crime Pattern Theory, wherein they suggested that crime is more likely to occur in areas where the offenders’ awareness space and perceived suitable target intersect (Rossmo, 2000). The specific target choice can alter depending on the interactions of the offender within their own physical and social environment (Brantingham & Brantingham, 1993).

Crime Pattern Theory uses concepts similar to those found in Rational

Choice and Routine Activity theories, with one important distinction. The theory is

not limited to the ‘who’ and ‘what’ of crime; instead, it expands our understanding of the concept of crime and place by utilizing both spatial and decision-making processes to explain the distribution of offenders, targets, and guardians. Though the theory borrows from Routine Activity and Rational Choice theories, its foundations are also based on concepts from the Geometry of Crime

(Brantingham & Brantingham, 1993).

One of this theory’s foremost assumptions is that crime is not random, and it does not occur uniformly across space and time (Brantingham & Brantingham,

1993). If crime is not random, then it must be at least partially predictable based on the patterns created within a person’s physical and social environment. The term pattern specifically describes the connections (physical or conceptual) of the objects, processes, or ideas (Brantingham & Brantingham, 1993). Utilizing such connections, patterns of crime or of criminal behaviour are analyzed throughout space and time.

As Eck and Weisburd suggested in 1995, the interactions of offenders within this physical and social environment are what influences an offender’s choice of targets. This interaction can be extremely complex, and many factors must be understood in order to accurately assess the patterns created.

According to the Brantinghams (1993), the likelihood of a criminal event occurring is dependent on the following factors:

1. Backcloth (i.e., activity or structure);

2. Site (i.e., selection);

3. Situation (i.e., guardians);

4. Individual Readiness (i.e., motivation);

5. Routine Activity Patterns (i.e., routine movement patterns); and

6. Distribution of Targets (i.e., hotspots, generators, and attractors)

(p. 266).

A convergence of good opportunities, good suitable targets, and a motivated offender acting within their own awareness space should theoretically be a good predictor of crime. Such convergence leads to ‘typical’ crime patterns being created. It is the existence of this convergence that lends credence to the spatial analysis of criminal events.

3.3 Summary & Application

What is apparent throughout the theories above is that crime and

criminality must both be considered as we attempt to decipher the environment’s

spatial affect on them. The focus of this thesis was on existing patterns of crime.

However, patterns only exist based on the convergence of human and

environmental interactions. Researchers have tried to understand how location

influences crime, why crime tends to cluster in certain areas, and how the

physical and social characteristics of place alter the potential for crime to occur

(Eck & Weisburd, 1995). In the end, the focus is not to test individual motivations,

but rather to accept that much research and theory have demonstrated the applicability of using geography in the analysis of criminal events.

The following chapter presents a case study that specifically examined the literature regarding the spatial and temporal dynamics of both static and dynamic crime, an overview of this study’s methods and procedures, and finally, a detailed review of the results of both the exploratory and the geostatistical analyses.

4: CASE STUDY

As was noted previously, only two studies have conducted geostatistical analysis, specifically Kriging, within the field of criminology (see Kerry et al., 2010 and Camara et al., 2004). The principal goal of this research was to address this deficiency in criminological research (Kerry et al., 2010) by creating a geostatistical model that used crime data to create more robust models that will ultimately enhance public safety by increasing our ability to predict criminal behaviour. Specifically, the three main objectives of this case study include the following:

1. Create a geostatistical model of two types of crime – break-and-

enter (static crime) and assault (dynamic crime) – to determine

whether the use of geostatistics, specifically Kriging, might

generate valid risk surfaces using criminological data.

2. If the model worked as anticipated, we would then determine

whether it more accurately predicted static or dynamic crime using

correlational analysis.

3. Finally, we would determine the feasibility of replacing the current

software that is operationally more complex with the simpler

software developed specifically for this study; Crime Risk

Assessment Software was designed primarily to create such

predictive models.

The case study described below draws upon theory and literature to achieve these goals, and it is comprised of three main sections. The first is a literature review of both the static (assault) and the dynamic (break-and-enter) crime, which presents an overview of the spatial and temporal considerations of each crime prior to analysis.

A detailed methodological approach to this study comprises the second section. It includes an overview of the sample, data, and software used, along with a detailed review of the particular statistics that created the robust predictive model for this study.

This case study’s comprehensive third segment summarizes the results by categorizing them into three sections: assault model results (point and polygon), break-and-enter model results (point and polygon), and a test of a comparative model.

A crucial first step was to examine the literature in this area. Section 4.1 provides a detailed overview of the spatial, temporal, and demographic considerations of both static (assault) and dynamic (break-and-enter) crimes.

4.1 Static & Dynamic Crimes

The objective of this thesis was to study techniques involved in the spatial and temporal analysis of crime, thus it was important to choose two crimes that reflected the elements studied (i.e., static and dynamic crime). As was previously described, a static crime has a stationary component (i.e., the crime occurs in one spatial location), whereas a dynamic crime is mobile, as it can occur in many

locations spatially. The static crime chosen for this case study was residential break-and-enter, frequently referred to as burglary. The location of the crime is not mobile; it can only occur in fixed residential housing locations. Assault was chosen to represent the dynamic crime, and an assault occurs between two or more people. The people are mobile and, while the crime’s location is fixed, the event could hypothetically occur anywhere spatio-temporally. The following chapter reviews the temporal characteristics of both crimes while examining the spatial and demographic dynamics of each.

4.1.1 Residential Break & Enter

People generally come home at night, lock their doors, shut their windows, close the garage, and perhaps turn on their security lights or set their alarms before going to bed. These routines are generated both by uncertainty regarding the risk of becoming a break-in victim and as an attempt to self-protect. Common talk indicates that much has changed over the past 20–30 years: we used to leave doors unlocked, kids played unsupervised in the streets, and garage doors were left open without fear of theft. As researchers, we now know the statistical chances that our home will be broken into: 700 general break-ins occurred in

Canada per every 100,000 people; and approximately 60% (420) of those were classified as specifically residential (Dauvergne, 2007). Saskatchewan, in particular, has a much higher than average rate of break-and-enters (1,147 per

100,000 people [Dauvergne, 2007]). This higher figure translates to approximately 688 residential break-ins per 100,000 population. For the purpose of making comparisons, the general break-and-enter rate in the United States is

2,690 per 100,000 (Bureau of Justice Statistics, 2009). Applying a similar 60% ratio of domestic break-ins generates a figure of approximately 1,614 residential break-ins for every 100,000 persons (Bureau of Justice Statistics, 2009).

These are very disturbing statistics, but do they mean that we are all equally vulnerable to being a victim of a residential break-and-enter? In order to answer this question, break-and-enter is discussed in terms of opportunity, motivation, and target selection. Specifically, we must understand how the selection criteria commonly involved in static property crimes differ from those that determine dynamic personal crimes such as assault.

As mentioned in this study’s background section, crime can be understood using perspectives from many different theories. Some of the more prominent theories treating opportunity, motivation, and target selection are Routine Activity

Theory and Crime Pattern Theory, both of which fall under the rubric of

Environmental Criminology, as discussed in Chapter 2.

Environmental criminologists assert that the willingness to commit a crime at a specific location includes interaction between a motivated offender, a suitable target, and the intended target’s lack of a guardian (see Felson & Clarke,

1998; Brantingham & Brantingham, 1993; Rossmo, 2000). Therefore, the decision to commit an offence would depend on the offender’s perception of the ease with which they may be able to break into the home, the value of the items that could be realized by stealing from that home, and the risk of detection or apprehension (Clarke, 1997, as cited by Sorensen, 2004).

From an Environmental Criminology viewpoint, when an offender plans to

commit an offence, many different factors contribute to their decision-making

process. These may include whether there are signs of occupancy (such as

noise, lights, or cars in the driveway), whether there are indicators of capable

guardians (which include any neighbours that may be present) (Sorensen, 2004),

evidence of large dogs, or an active alarm system display. Other factors include

the time of day (e.g., lighting) and time of year (e.g., school or work days). Based

on these predictive factors, it is apparent that break-and-enter can include

elements of planning in addition to being a crime of opportunity. If the opportunity poses a high risk, it is less likely that the offender will select that site; they may instead choose another location providing better cues. However, if such factors

produce a lower probability of detection and prove to be a suitable target

otherwise, the home is more likely to be chosen.

As Goodwill and Alison indicate, the most effective way to link offences is

to utilize “1) geo-spatial information, 2) temporal aspects, 3) behavioural

characteristics and lastly, 4) dwelling characteristics” (2006, 12). A combination

of these four linkages, coupled with an understanding of environmental cues and

of the crime site (see Brantingham & Brantingham, 1978), lead to a

comprehensive understanding of site selection. The following section introduces

current literature related to these areas, focussing particularly on geo-spatial

information and temporal aspects, though behavioural and dwelling

characteristics are also discussed to provide context to the overall geographic

analysis.

4.1.1.1 Geo-Spatial Information (Target Selection)

In concordance with the propositions of Environmental Criminology and

using the distance decay model, an offender is more likely to commit a crime

within a 1.5 to 2 mile radius of their residence (as delineated by the estimations

of decay below).

Figure 3 Distance Decay Re-Examined (Rengert et al., 1999 435) Aggregate Distance-Decay Function 60

Mean Number Number of Mean Crimes 10

0 0-1.0 1.01-2.0 2.01-3.0 3.01-4.0 4.01-5.0 5.01-6.0 6.01-7.0 7.01-8.0 Distance Bands (in miles)

More specifically, burglary targets are “usually found by offenders attuned to their surroundings during the course of their daily routine activities, and then intermittently watched” (Rossmo, 2000, 136). As the Brantinghams (1981)

pointed out in Crime Pattern Theory, this processing of routine activities in one’s

environment creates a mental map based on experiences among one’s familiar

surroundings. This “mental template” created during an offender’s routine spatial

movements will include information based on their preferred target locations, travel distance, and topographic information (Brantingham & Brantingham, 1981).

Goodwill and Alison (2006) have also suggested that offenders not only collect geo-spatial information to form mental maps, but that this information encourages the offender to commit a crime in familiar, rather than unfamiliar, areas. This mental map is developed through a process of familiarity based on the triangulation of the offender’s work, play, and residence (also known as their activity nodes).

Within this familiar area, the offender is able to watch their targets and wait until an opportunity presents itself. As well, Clarke and Hope (1984) pointed out that if the burglar’s first attempt within these familiar surroundings is successful, the offender may be encouraged to re-offend there.

Mental maps are not the same for each offender. Canter and Gregory

(1994) suggest that the spatial information contained in an offender’s mental map is particular only to that offender. Therefore, the actual area where the burglary is committed can reveal clues not only about the probability of other burglaries being connected to it, but it may also provide clues regarding the general area in which the offender may reside.

The notion of distance travelled to the crime location has also been examined. In comparison with other crimes, a study conducted by Goodwill and

Alison (2005) indicated that the patterns of crimes such as burglary, rape, and murder will all vary as a function of three factors that influence offenders’ mental maps. These include:

1. “First, offenders will likely be influenced by the dynamic nature of

targets in rape and murder in contrast to the static nature of targets

in burglary.

2. Second, it is posited that offenders will differentially attack targets

based on specific characteristics of the target or of the location, and

that this difference will be evident across crime types.

3. Finally, the risk and gravity of attacking different targets at different

locations will lead to differences in spatial patterns between

offender types.” (Goodwill & Alison, 2005, 161-62).

Just as the model suggested by Goodwill and Alison supports the mental map concept, so does it also support the notion of Routine Activities Theory–the presence of a suitable target (within their activity space) and a lack of guardianship (less risk) combined with the motivated offender will reinforce this template.

4.1.1.2 Dwelling Characteristics (Situation)

Not only are familiarity with the area and the distance travelled to the crime important, but the characteristics of the target dwelling also affect the selection process. As mentioned previously, researchers tend to believe that break-and-enter is a product of reinforced mental maps, but there is also an element of opportunity. Though the act itself is most often calculated, if a ‘good’ opportunity presents itself, a motivated offender may react spontaneously.

Opportunities are typically based on the characteristics of the dwelling and

the lack of a guardian (low risk). Specifically, Cromwell et al. (1991) found that

the offender’s decision to target a location was primarily based on environmental

cues that demonstrate an immediate consequence (reward). For example, if an

offender has successfully broken into houses through open garages in the past,

the unexpected appearance of a house with an open garage and no guardian (no

cars or other indicators that family members are present) may reinforce the

template and facilitate the crime being committed again. Cromwell (1991) also

pointed out that the consequence for the action must be immediate rather than

long term. For example, the risk versus gain equation is based on the immediate

monetary reward rather than the concern of being convicted for a crime.

According to Cromwell (1991), these immediate risk versus gain cues are based on three environmental cues: surveillability, occupancy, and accessibility.

Surveillability refers to how well the residence can be overseen by neighbours or

people passing by, the visibility of the house and its proximity to the road or

neighbours, as well as landscape characteristics such as shrubs, trees, lighting,

etc. (Cromwell, 1991). The less visible the house is to others, the more target

potential it has.

The second category of risk cues surrounds occupancy. For typical

offenders, an occupied home is a deterrent because of the increased likelihood of detection. Signs of occupancy include cars in or near the location and noise or other signs of someone being present (Cromwell, 1991). Interestingly, in a study conducted by Wright et al. (1995) on target selection, when comparing burglar

responses to a control group, the presence of a car at the dwelling did not necessarily deter them as much as the presence of an alarm, a lock, or a dog.

The third set of environmental cues involves the accessibility of the house.

Accessibility includes things such as locks, fences, alarms, dogs, walls, etc.

(Cromwell, 1991). According to Cromwell (1991), all of these environmental cues affect the offender’s decision-making framework to commit a crime. As seen in the target site selection diagram below, if an offender successfully uses this template, then just as with the concept of mental maps, it reinforces the template for success, and we can expect the offender to commit similar crimes in similar situations because their template worked.

Figure 4 Reproduction of “The Decision Process in Target Selection” (Cromwell et al., 1991, 39)

Do the immediate gains outweigh the immediate risks?

Assume minimal expectations of gain

Use "argument by contradiction" and search for immediate risk cues

Are there accessibility Are there surveillance Are there occupancy cues to contradict cues to contradict cues to condradict ENTRANCE IS TOO SOMEONE WILL SOMEONE IS HOME? DIFFICULT? REPORT ME?

Abort Completely; or abort and return later; Burglarize target site or displace to new target site

4.1.1.3 Temporal Aspects

Time also plays an important role in assessing target selection. Many studies find high concentrations of break-and-enter during certain points in the day. However, the studies do not all agree on exactly when those timeframes

occur. Possible explanations for this divergence include the fact that studies are done in different geographical locations where time of day is affected by location

(e.g., compared to North Americans, Europeans have different coffee break periods and different school and work hours) or by the fact that temporal aspects change with the seasons (i.e., as daylight hours and weather patterns change, burglary patterns also change). As well, as some of the studies below discuss time, it is important to note that some temporal variations are the result of the type of data collected. It is not always clear if researchers used reported time or actual occurrence time.8

A study conducted in Denmark found that offenders commit less crime during the spring and summer months (42%) than they do during the fall and winter seasons (58%) (Sorensen, 2004). They also found that the four most frequent break-and-enter days in 2002 were December 23, 24, 25, and 26

(Sorensen, 2004). Interestingly, in a 2000 study conducted by Cohen and Rotton, the most frequent break-and-enters for Monday thru Thursdays occurred between 3:00 pm and 9:00 pm, whereas Friday to Sunday showed a higher frequency of break-ins between 9:00 pm and 3:00 am. Research conducted by

Boba (2009) describes one study where the most break-and-enters occurred

Monday to Friday from 10:00 pm to 4:00 am, but that study did not specify the day of the week. These research studies are discussed in the results segment of this paper, as these peak time periods are fairly consistent with the results outlined here.

8 In this study, time is reported in ‘incident report time’.

North American statistics indicate that break-and-enters occur in Canada at a rate of 420 per 100,000 population (Dauvergne, 2007), and in the United

States at a rate of 1,620 per 100,0009 (Bureau of Justice Statistics, 2009). As

Rengert and Wasilchick (1985) point out, time patterns of break-ins are based on the victims’ time patterns. For example, break-ins are higher in daytime periods when victims work at typical 9-to-5 jobs or have gone out for the evening.

However, these patterns are not consistent with every offender, and thus can also provide insight into the offenders’ lifestyle and type (Wasilchick (1985).

Specifically, Bennet and Wright (1984) identified three categories of offenders: planners, opportunists, and searchers. They discovered that planners outline the offence in advance, whereas opportunists respond to environmental cues and offend when the template fits their intentions (Bennet & Wright, 1984).

Searchers, on the other hand, seek out a target and offend whenever they find a suitable one (Bennet & Wright, 1984). Therefore, the time of day that an offender breaks into a residential location depends upon the type of offender (i.e., opportunistic, searcher, or planner), as well as the time patterns of the victims.

Despite all these categories of offending, as Cohen and Rotton (2000) pointed out, the key factor associated with break-and-enter is the lack of a capable guardian. The possibility of someone being home or of someone being able to see the offender breaking into a residence drastically reduces the likelihood that the offence will occur.

9 1,620 is determined by approximating 60% as the number of break-and-enters that are residential.

4.1.2 Assault

Unlike the plethora of research conducted on break-and-enter, assault literature is relatively deficient in terms of the quantity of research conducted on common assault in particular. Abundant research has been conducted with respect to specific sub-groups of assault research (domestic violence and sexual assault offer two examples of well-researched assault sub-types), but this is not the case with common assault. Therefore, this section provides an overview of the spatial, temporal, and offender characteristics of common assault based on the current literature available.

4.1.2.1 Spatial Dynamics of Assault

Assault was chosen for this study due to this crime’s high mobility (i.e.,

dynamic) factor. Unlike break-and-enter that occurs in a static, unmovable

location such as a residence, assault can theoretically occur anywhere in space

and time (bound by environmental factors, i.e., lakes, mountains, etc.). In further

contrast to break-and-enter, assault most commonly occurs amongst people who

are known to each other or have some type of association (Holzman, 2001),

whereas break-and-enter typically involves a victim who is completely unknown

to the offender (and furthermore, usually unseen). Despite the dynamic nature of

assault, however, it is not necessarily an event that happens anywhere. Rather,

and consistent with Crime Pattern Theory, the concentration of assaults

historically produces “hot spots,” or locations where these criminal events

frequently tend to cluster (Suresh & Vito, 2007).

Not so dissimilar to break-and-enter, however, is the concept of capable guardians. Holzman, Hyatt, and Dempster (2001) pointed out that the presence

of a guardian may in fact reduce the likelihood of assaults occurring in public,

and assaults may therefore occur more often in the privacy of one’s own home.

However, factors such as alcohol and drugs can more often supersede this

notion of a guardian, allowing people to commit assault without fear of being

caught. This is why drinking establishments still tend to exhibit higher

concentrations of assault than do residential locations.

When analyzing the spatial dynamics of assault, the most common places

that come to the minds of most regular citizens is that they occur at drinking

establishments. A study surrounding the density of bars in relation to assaults

was conducted by Lipton and Gruenewald (2002), who found that the density of

bar locations was strongly associated with higher rates of assault, whereas a

higher density of restaurants was negatively associated with violence. Similarly,

Michael Livingston (2008) found that the density of establishments serving

alcohol produced higher concentrations of assault.

With rare exceptions, there is generally a clustering of drinking

establishments located within the perimeters of a city’s lower socio-economic

status (SES) areas. Some research has demonstrated high correlations not only

with licensed establishments (Livingston, 2008), but also with the socio-economic

characteristics of the neighbourhood. Other studies find assault associated with

youth, drinking, city centres, and entertainment districts (Felson R. B., 1997;

Bromley & Nelson, 2002; Lee, Akers, & Borg, 2004). For example, Richard

Felson (1997) found that males with an active nightlife were at increased risk both of becoming a victim and of being involved in violent interactions, generally.

While Bromley and Nelson (2002) found that the majority of violent alcohol- related offences occurred in the city centre and at night. All of which is supported by the concept of Routine Activities Theory in which the convergence of individual patterns spatio-temporally, can lead to a higher risk of becoming a victim or involved in violence (Felson, 1997).

Several studies have also focussed on the effect of public housing on higher rates of assaults. For example, Holzman et al. (2001) conducted a study on the aggravated assault patterns in public housing in two unnamed US cities

(City x and City y), focussing specifically on place, gender, and race. They hypothesized that rates of assault would be higher in public housing areas as compared to the rest of the city, while also assuming that women experienced a higher risk of assault than males in these areas (Holzman et al, 2001). Using City

X and City Y as a comparison, results indicate that the rate of aggravated assault was higher for public housing residents in comparison to elsewhere in the city.

Specifically, the year the study took place, the rate of assault for both jurisdictions was 3.9 per 1,000 populations, whereas the rate of victimization for black females in City X in public housing areas was 5.3 per 1,000; for city Y, it was 21.1 per 1,000, which was nearly 4 times City Y’s overall rate (Holzman et al., 2001).

A 2007 study conducted by Suresh and Vito in Louisville, KY, provided similar results in that they found the presence of lower income, or public housing

increased the risk of assault; the concentration of instances of assault was higher

in areas encompassing low-income, public housing. Suresh and Vito also

analyzed rates of assault in public housing units, and compared it to the rates

occurring after one such unit had been demolished and relocated. Once it had

been demolished, the high assault cluster areas lessened substantially before

increasing in other public housing areas to which the residents had relocated

(Suresh & Vito, 2007). In addition to researching low-income public housing

areas, the influence of other characteristics of assault (e.g., day, time,

demographics, and temperature) have also been studied.

4.1.2.2 Temporal & Temperature Characteristics of Assault

There are several theories regarding the impact temperature has on crime; specifically, the incidence of certain crimes increases as the temperature rises. In particular, Rotton and Cohen (2004) demonstrated a positive

relationship between temperature and assault according to temporal and

seasonal variations. Rotton and Cohen (2004) examined the impact climate control might have on assault, controlling for indoor and outdoor temperature variations (e.g., air conditioning, fans, etc., produce one form of climate

controlled location). Their study analyzed the number of service calls made to

Dallas police departments between 1994 and 1996. Their findings suggest that

assaults occurred less often in climate-controlled areas than in non-climate-

controlled locations (Rotton & Cohen, 2004). Specifically, the average number of

assaults nearly doubled when the temperature was between 75 and 95 degrees

Fahrenheit (Rotton & Cohen, 2004).

They also discovered interesting correlations between criminal activity and holidays and time of day. Specifically, assaults tended to increase on two specific holidays: Memorial Day (around May 30, depending on the year) and

Independence Day (July 4) (Rotton & Cohen, 2004), both of which are warmer holidays than are Thanksgiving and Christmas. In addition to these temperature- based correlations, they found that the best predictor of assault was the time of day. Specifically, more assaults occurred in non-climate-controlled settings between 3:00 am and 8:59 am (Rotton & Cohen, 2004). Interestingly, bars typically close between 2:00 am and 3:00 am, and though it was not tested in the original analysis, the spill-over from assaults related to alcohol and drug consumption may have affected their study. For example, consistent with Routine

Activity Theory, the convergence of a motivated offender (possibly an intoxicated individual), a suitable target (confrontation leaving a drinking establishment), and lack of capable guardians may explain such results.

Keith Harries (1989) conducted a study that demonstrated a correlation between the time of day and the number of assaults; assault levels were highest during the summer months when average temperatures exceeded 80 degrees

Fahrenheit. Harries also found that assaults occurred most frequently on weekends and in the late evening hours. Though temporal and temperature characteristics provide some insight into assault levels, it is similarly important to analyze these offences’ demographic characteristics.

4.1.2.3 Demographic Characteristics

Demographic characteristics of the victims and offenders provide the final key in analyzing patterns of assault. Holzman, Hyatt, and Dempster (2001) found that Black people were victimized much more often than White, and that Black females had the highest victimization rates of all demographic groups (Holzman et al., 2001). Black females also had the highest rate of victimization at the hands of an intimate partner, whereas Black males were most likely to be victimized by a stranger, both in public housing locations and throughout the city (Holzman et al., 2001).

Keith Harris (1989) found that the highest assault rates occurred in low socio-economic areas, with the highest rate of assaults occurring for victims aged

25 to 34. When comparing low versus high socio-economic areas, Harris also found that victims’ residences and street-based assaults occurred at a higher rate in low SES locations, but that in medium SES locations, bars, playgrounds, and other locales were more likely to be the sites of assault than were low SES locations, a surprising result (Harris, 1989).

4.1.3 Summary

Both break-and-enter and assault crimes involve interesting, if somewhat distinct, spatial, temporal, and demographic characteristics. Static crime is more consistent with decision-making that involves planning, thought, and attention to detail than is assault that is consistent with affect, particularly those affect impacts of alcohol and drugs. In both categories, the presence of a capable guardian or of surveillance may tend to reduce the likelihood of the crime

occurring. However, as was the case in the research above, the impact of alcohol or narcotics may override the guardianship concern.

Discussion of these crimes’ spatial and temporal considerations provides insight into patterns we may expect when creating a geostatistical predictive model of crime. Section 4.2 provides a detailed outline and explanation of the specific sample, programs, and particularly the statistics used to analyze these two crime types.

4.2 Methods & Procedures

This study’s objective was to apply new geostatistical models, specifically

Kriging, to test crime data. The methods section addresses the chosen complexity models, statistics, and procedures. It reviews three primary elements:

1. sample datasets, along with a brief overview of the study area;

2. GIS software, ArcGIS, and the Geographical Crime Risk Assessment

Software designed for this study;

3. techniques and procedures used.

4.2.1 Sample & Study Area Overview

The sample obtained for this study was secondary data obtained from the

Regina Police Service in Saskatchewan, Canada. This was an exhaustive sample comprised of two separate datasets for the period studied (2005). The first dataset contained 4,173 cases, a static sample that included all of the residential and commercial break-and-enters reported in the City of Regina in

2005. Owing to the different spatial dynamics of residential versus commercial

break-and-enter and the fact that these types have very different geographic

profiles, it was determined that only one type should be used to create a spatial pattern. The final sample was reduced to N = 1,875for the period spanning

January 1 to December 31, 2005. It included all residential break-and-enters for the City of Regina. Within this dataset, each specific case contained the associated occurrence identification, the date, and the location of the occurrence, along with the potential offender’s home address (if known), and if a suspect had been arrested, their personal identification number.

The second dataset consisted solely of assault cases (classified in this study as dynamic crime) from the City of Regina Police Service. The total sample contained N = 2,197assault cases occurring from January 1 to December 31,

2005. It included all forms of assault, including domestic, with the sole exception

of sexual assault. Within this dataset, each specific case also contained the

associated occurrence identification and the date and location of the occurrence,

along with the potential offender’s home address and personal identification

number in cases where a suspect had been arrested.

In order to analyze the data, the addresses from both the assault and the

break-and-enter data had to be correctly geocoded. Geocoding data into ArcGIS

entailed a process of the software allocating x and y coordinates for each

address in order to create a visual depiction of it on a basemap (Thompson,

2003). The addresses of both assault and break-and-enter data were extracted

from the Regina Police Service’s database and geocoded into point data so they

could be analyzed using GeoPinPoint Suite geocoding software.

Following this geocoding process, the data were exported to a Statistical

Package for the Social Sciences (SPSS version 13) in order to split the two types

of crime into separate model and test groups. The geographic models were built on 70% of the data. The remaining 30% were used to test the likelihood of the predictive validity of the model. That is, SPSS was used to randomly select and

extract 30% of both assault and break-and-enter cases, a process which resulted

in the following four distinct databases:

1. Assault Model 70%;

2. Assault Test 30%;

3. Break-and-Enter Model 70%; and

4. Break-and-Enter Test 30%.

Finally, these datasets were summarized by address in order to create a z value

of intensity (e.g., number of times the same crime happened at a specific

location), leaving a total of eight separate databases, as depicted in the table

below. The following tables outline the exact sample size of each database

including single point data and summarized point data.

Table 1 Model and Test Databases for Assault and Break and Enter Single Point Data Model Test Single Point Single 70% Single 30% Total Assault n = 1559 n = 638 n = 2197

Break & Enter n = 1291 n = 584 n = 1875

Table 2 Model and Test Databases for Assault and Break-and-Enter Aggregate Point Data Model Test Aggregated

Aggregated 70% Aggregated 30% Total Assault n = 1176 n = 561 n = 1737 Break & Enter n = 1215 n = 567 n = 1782

After the point data were geocoded, the data were aggregated further to a polygon level in order to illustrate the point data (i.e., crime) in a geographically bounded area (Eck et al., 2005). It is important to note that the data were not aggregated for the geostatistical process (this only utilized point data); rather, it was done for exploratory purposes. Because this study tests different methodological approaches, it was important to not only utilize point data and

Kriging to produce a predictive model, but also to conduct polygon level and other local and global tests to provide a more exploratory, comprehensive review of the data.

During the aggregation process, the data were assigned a number corresponding to its Digital Boundary File (DBF). A DBF is a polygon theme overlaid on the basemap (Thompson, 2003). This file delineates the boundaries of the neighbourhoods for the City of Regina and allows other data to be cartographically displayed.

Upon completion of this process, the point data, along with any other data converted in this manner, could be displayed as part of a continuous, two- dimensional surface that varied between different polygons (neighbourhood boundaries). The polygons were arranged geographically. Therefore, the original point data for both assault and break-and-enter were converted into polygon level

data in order to perform some basic geographical descriptive analysis on both

types of data; this process is discussed in more detail in section 4.2.6.

Access to the descriptive census data needed to explore the polygon

crime data using neighbourhood boundaries was facilitated through Mount Royal

Library Administration.10 Census neighbourhood boundaries were chosen on the

basis of the relative size of the cities available for study. Given that modifiable

areal unit boundary issues11 can be affected by areal analysis that is too large or

too small, the most useful choice for descriptive analysis in a city the size of

Regina was neighbourhood boundaries.

4.2.1.1 Data Privacy and Confidentiality

Privacy and confidentiality were maintained throughout this study. In order

to ensure the privacy of the offenders and the victims, the Regina Police Board

agreed to remove identifying information from the data, including the names of

both the offenders and the victims. However, as this was a geographic analysis

of specific crimes, the Board did agree to provide the offender’s address and the

address/location of the criminal event. It was also agreed that the data would be accessible only to the researcher, that the data would not be used for any purpose other than this research study, and that a copy of this study would be provided to the Board.

10 Polygon boundary files were provided by Natalie O’Toole from the Library Administration at Mount Royal University. 11 Modifiable Areal Unit Boundary Problem (MAUB) is in regard to the analysis of spatially aggregated data (areal/polygon level data). A problem with areal measurement is that the crime is aggregated to a boundary level; however, if crimes occur along area boundaries or intersection boundaries, analysis may either not be accurate, or it may not be accurately represented geographically (McLafferty, Williamson, & McGuire, 2000).

In order to maintain confidentiality and protect the data, it was agreed that the researchers would:

“(a) only access the data from a computer located in a physically

secure environment;

(b) not disclose the data to third parties without the prior consent of

the Board;

obtained for the research, with the exception of one archived copy.

The archived copy would be maintained for a period of five years, in

accordance with standard research data retention guidelines. The

researchers would notify the Board in writing if any archived data

had to be retained beyond the five-year period” (Data Sharing

Agreement, Appendix B).

For a more detailed outline of the privacy and confidentiality data sharing agreement, refer to Appendix B. Prior to discussing the statistical procedures, a brief overview of the study area is provided.

4.2.1.2 Overview of Regina, SK

The City of Regina is located in Saskatchewan, one of the Prairie

Provinces of Western Canada. The city, which has an area, of 3,408 square kilometres (B.C. Stats, 2007), is home to the University of Regina and to the

Roughriders Canadian Football League team, but it could be argued that it is most famous outside of Saskatchewan for its proximity to the town of Rouleau

(roughly 45 miles southwest of Regina), home to the comedy series Corner Gas.

Overall, the population of Regina is relatively small, as only 194,971

people resided within the census metropolitan area (CMA) in 200612 (Statistics

Canada, 2008). Of these, slightly over a quarter (28.3%) are believed to be under the age of 19, while the remaining 71.7% of the population, being over the age of

20, are considered adults. The population is comprised of an almost equal number of males (49%) and females (51%) (B.C. Stats, 2007).

Of the 18,635 census families within Regina, approximately 77.7% (n =

14,475) are dual-parent families, while approximately 22.3% (n = 4,160) are

reported to be single-parent families (B.C. Stats, 2007). Of that population of

census families, 55% of individuals over the age of 15 are married or living in

common-law relationships, while 30.6% have never been legally married

(Statistics Canada, 2008).

The total number of private households in Regina is 26,675, and each

household contains, on average, 2.4 individuals (Statistics Canada, 2008). Of

these private households, 18,800 (70.5%) own their home, 6,820 (25.6%) rent

their accommodations, and 1,050 (3.9%) live in band housing (B.C. Stats, 2007).

The median family household income is $55,629; the median income for males is

$34,954, while it is only $25,098 for women. Of the persons not in economic

families, 32.3% fell into the low-income category, and 9.1% of economic families also belong in this category (Statistics Canada, 2008).

12 Statistics Canada only produces census results every five years, thus the statistics reported here are from 2006. However, there were only very minimal demographic changes within that year in Regina. Thus, given the descriptive nature of this informative segment, using the 2006 profile was deemed sufficient for our purposes.

With respect to immigration, 97.3% of Regina’s populace are Canadian citizens, and 9.1% of those consider themselves either immigrants or recent immigrants (Statistics Canada, 2008). Of Regina’s citizens, 8.9% report being

Aboriginal, while 6.6% claim visible minority status (Statistics Canada, 2008).

Finally, in regard to the total population, the unemployment rate in Regina in

2006 is reported to be 4.8%, whereas the rate of employment was 67.5%

(Statistics Canada, 2008).

Turning now to the city’s overall context, Regina’s inhabitants account for approximately 20% of the entire province’s population, although in the past, it has been one of the few Canadian cities to consistently report a decline in population

(Wallace et al., 2006). Despite the fact that Regina is only the eighteenth-largest city in Canada (Wallace et al., 2006), it was reported in 2006 that Regina had the highest crime rate in Canada for nine of the last ten years (Wallace et al., 2006).

Furthermore, Regina’s crime rate has consistently, and considerably, exceeded

Canada’s average crime rate for more than the past ten years. The City of

Regina’s high crime rate per capita and its negative growth rate, when combined with the populace’s consistently low income and rate of employment, provide a base for productive and positive research.

4.2.2 Software

Analysis for this case study was conducted using two different geographic information system software products. The first software, ArcGIS 9.1, facilitates the basic geocoding, cartographical representation, and analysis of all of the

spatial data. The second, Geographical Crime Risk Assessment Software,13 is a specialized crime risk prediction software created specifically for this study. Both products were used to illustrate different techniques available for predicting crime. The next two sections provide an overview of each software package and highlight the positive and negative aspects of both geographical information systems.

4.2.2.1 Geographical Crime Risk Assessment Software

The Geographical Crime Risk Assessment Software is a new product created at Mount Royal University by a team of researchers. Its purpose is to create a risk analysis tool that will be both easier to use and more functional for crime analysts and members of law enforcement. The software treats the locations (i.e., assault locations) as input pairs to a function. The function values are all equal to 1 for all locations, and each indicates that a crime occurred there.

After assigning a value to each instance, a Delaunay triangulation is applied to the data. Delaunay triangulation refines the triangulation multiple times until the outcome is below the pre-determined threshold. The threshold is determined based on the level the user desires for their final grid.

Specifically, triangulation is used to predict the risk of a criminal act occurring by assessing the centroids of the triangles along with the midpoint of the edges (Zizler). This centroid value x = (x,y) is:

13 Development of the Geographical Crime Risk Assessment Software was begun in 2006 by the following: Petr Zizler, designer, Department of Mathematics; Nikki Filipuzzi, principal researcher for this study, Justice Studies; Dave Dever and Laura Marik, programmers; Patti Derbeshyire, project coordinator, Business Department; Natalie O’Toole, GIS specialist, Library Services; and John Winterdyk, Justice Studies. It has since been developed into a working beta product which is currently undergoing a testing cohort.

Equation 5 Centroid Calculation (Zizler, 2008, 2)

Where:

= is the distance to the nearest vertex in the triangle

= is the risk at the vertex

After determining the centroid, the same calculation is then used to determine the midpoint of the edge, seen as:

Equation 6 Midpoint Calculation (Zizler, 2008)

Where:

= the distance to the vertex in the edge

After calculating the centroid and midpoint, it is then refined with several iterations, thus creating a risk surface. The risk surface is then smoothed by using wavelet smoothing to produce a geographic depiction of high and low crime risk by colour.

Delaunay triangulation is a way to improve upon Kriging computing efficiency (Hessami et al., 2001). With simple Kriging, there is always a difficulty with the estimation of Z at a specific location (Hessami, et al., 2001). The use of

Delaunay triangulation in Kriging application greatly reduces computational cost

and estimations that are dependent on the observations specific to its

neighbourhood (Hessami et al., 2001). With this new program, we are able to

compare different crime risk surfaces over time. It enhances regular GIS software

by providing a risk-related learning function. Using such a learning function, we

expect to be able, in the future, to estimate the amount of risk inherent in any

given area for the upcoming year based on attributes from a previous crime.

The Geographical Crime Risk Assessment Software operates according to a Visualization Toolkit Application (VTK), which is an open source software system used for modelling and image processing that also provides 3D computer graphics and information and scientific visualization (Kitware, 2008). A major

difference between the Geographical Crime Risk Assessment Software and other

products (such as ArcGIS) is the use of Wavelet Theory when mapping crime.

Previously developed software does not incorporate wavelet analysis, which

utilizes a scalable modulated window that is shifted along a signal to calculate

the spectrum at every position (Zizler, 2007). Over many repetitions, or iterations,

“the result is a collection of time-frequency representations of the signal, all with

different resolutions [multi-resolution analysis]” (Zizler, 2007, 1).

The benefit to using this multi-resolution Wavelet Theory is the ability to

look at points (in this instance, crime points) from both large-scale (coarse) and

small-scale (fine) vantage points (Zizler, 2007). Such scalability allows for

zooming while the interpolation process is being conducted. Ultimately, this

wavelet decomposition series leads to a:

“unique [surface] from conventional surface creation because it

allows multi-resolution analysis, allows for the removal of

extraneous ‘noise’, allows the user to select the number of

decompositions based on the type of crime being analyzed, and

then makes it possible to reconstruct the surface without the

‘noise’” (Zizler, 2007, 1).

Though the benefits the Geographical Crime Risk Assessment Software offers

when compared with other packages appear sound, the software is still in the

infancy development stage, and some weaknesses must be noted. At the time of

writing, the benefits are only predictive. It is, however, anticipated that the

software will become increasingly functional as development continues. In the

meantime, software packages like ArcGIS (described below) still usefully perform

basic descriptive, spatial analysis on crime location data.

4.2.2.2 ArcGIS

ArcGIS is a geographical information system used to transform spatial

data into information (Demers, 2000) that can then be used for illustration or

interpolation. Geographic Information Systems (GIS) like ArcGIS contain

automated ideas and concepts from over 2,500 years of geographic research

(Demers, 2000). Originally developed for geographers, geologists, scientists,

etc., geographic information systems have been transformed and are now

utilized in many areas including criminology (Griffith, 2008). ArcGIS specifically offers literally hundreds of functions: data processing, aggregation, classification,

map production, networking, and temporal and spatial analysis, including point- and polygon-data analysis.

It far supersedes the capabilities of the Geographical Crime Risk

Assessment Software presented in this thesis, at least insofar as its preliminary stages of development demonstrate. However, ArcGIS is not a crime-specific analysis software. Many of the functions of ArcGIS, though very useful, are not applicable to crime analysis. For example, in this study, ArcGIS was utilized for the following functions:

1. Geocoding;

2. Defining nearest neighbours;

3. Point data analysis, including standard deviational ellipses and

Kriging; and

4. Polygon data analysis, including spatial autocorrelation.

One of the problems with ArcGIS is assessing crime hot spots or predicting high crime areas without over- or under-estimating as a result of modifiable areal unit boundary problems. This set of problems has yet to be resolved and will be discussed further in Chapter 5.

A final critique of using GIS systems such as ArcGIS is the difficulty the average researcher faces in using the program. It is highly complex and most find it difficult to maneuver within, from geocoding down to the actual analysis

(Griffith, 2008). Developing specific risk assessment software for crime may be valuable simply on the basis of the software system’s complexity. Geographical

Crime Risk Assessment Software was developed in order to assist in the

‘predictive’ forms of analysis for this study.

Despite these limitations, the benefit of using ArcGIS is the exploratory

and descriptive forms of point and polygon data. The procedures and techniques

used by both the ArcGIS and Geographical Crime Risk Assessment Software are

therefore outlined below in greater detail.

4.2.3 Techniques and Procedures

Successful risk models do not always rely on one statistical technique to

analyze a phenomenon. As outlined in Chapter 2, various forms of risk indices –

polygon mapping, dasymetric mapping, and Kernel smoothing – have been used

as tools to create risk models. These examples demonstrate the utility of using

multiple statistical techniques to create a robust predictive risk model. Statistical

analysis for this study utilized multiple techniques to produce risk models of static

and dynamic crime. The chart below illustrates the analytic process conducted.

4.2.4 Statistical Analysis

Analysis Process

ArcGIS Crime Risk Software

Point Data Polygon Data Geostatistical Point Data Analysis

Nearest Nearest Neighbor Neighbour kriging

Standard Deviational Spatial Ellipses Autocorrelation

Kriging

Statistical analysis for this study used the ArcGIS spatial analyst,

Crimestat,14 as well as S-PLUS15 and the newly developed Geographical Crime

Risk Assessment Software. After producing the geocoded data noted earlier, it was then displayed cartographically in both single (single z value) and

14 Crimestat III is a spatial statistics program used to analyze spatial crime data (Levine, 2004). 15 S-Plus is analytic software used to analyze, interpret, and graphically display both regular and spatial types of data (TIBCO, 2009).

aggregated point data form (also known as areal or polygon level data–multiple z values)16 in order to conduct spatial analysis.

When conducting spatial analysis, it is important to differentiate between

the types of analysis that can be performed. For example, analysis can be

categorized into three groups – global, local, and focussed statistics – but only

global and local statistics were relevant to this study. Global statistics determine

the amount of deviation from randomness that occurs in the data (Rogerson,

2001). By testing the data, global statistics are ultimately used to uncover overall

patterns. Local statistics, on the other hand, are more specifically used to

evaluate clustering around a geographic location (Rogerson, 2001), assaults

occurring near a bar, for example. If global statistics do not uncover a significant

deviation from randomness, local statistics may be utilized to evaluate clusters at

a finer, more detailed resolution. Owing to the differences in both techniques and

procedures, the next two sections detail the techniques and software used for

both single-point (point) and multi-point (polygon) level data at both a global and

a local level of analysis.

4.2.5 Point Data

As previously noted, point data are usually displayed cartographically by x

and y coordinates on a map. Each such coordinate represents one event. In this

case, that would represent the location of either a break-and-enter or of an

16 Polygon or areal data is single point data that has been summarized at a specific location. For example, if a store were robbed, it would be represented by a single x and y coordinate. However, if the store had been robbed five times within a year, all five points would be represented by one larger point indicating a single x and y coordinate with a designation of five robberies at that location.

assault, depending on the type of analysis. All of the methods below are

considered local levels of data analysis conducted on point location data for both

the break-and-enter and assault databases.

4.2.5.1 Visual Analysis

The first step in any geographic analysis of data is visual inspection

(Demers, 2000). After the data has been geocoded, they are depicted on a

surface representing the projected view of the resulting city or area being

studied. Once the point locations are illustrated on the map, it is important to

assess the data visually to ensure, at face value, that the data appears normal

and are not incorrectly projected or geocoded.17

Creating a bivariate representation of the x and y coordinates on a graph in S-Plus constitutes another form of visual analysis. This form depicts the

clustering of events within a bivariate graphical representation.

The final visual method used to verify the data in this study was to plot the data in the Geographical Crime Risk Assessment Software in point locations, and then use Delaunay triangulation to visually depict the patterns and clusters

(Hessami, et al., 2001) occurring within the city region. Prior to statistical confirmation of clusters, this method is useful for providing a general idea of randomness as compared to the clustering of data within a simple visual

17 The process of geocoding is conducted by a program which takes an address and attempts to map the address to an exact location. The problem is that street names can be spelled incorrectly or the address may be too new or not show up on a basemap being used to geocode for some other reason. Therefore, it is very important to verify some of the addresses to ensure incorrect geocoding has not occurred.

representation. and techniques were used in this case to determine whether

complete spatial randomness exists.

4.2.5.2 &

Both & produce plots of the empirical distribution function (EDF), but

the deals with the origin-to-point analysis, whereas the is a point-to-point analysis of the nearest neighbour distances for crimes in the study area

(MathSoft, 2000). and techniques were originally designed to analyze points

in spatial regions where the likelihood that an event will occur is distributed

evenly across a given region (Wimble et al., 2006). This spatial homogeneity

assumes similarity across space. For example, a star could theoretically be

located anywhere in space, just as a tree could grow anywhere in a forest

(Wimble et al., 2006). This assumption of similarity does not apply to the field of criminology, however. The following examples demonstrate that criminal behaviour cannot necessarily happen anywhere spatio-temporally. Break-ins involve a residence and are therefore restricted to anywhere housing is located, and assault requires a violent act to occur between two or more people, something which is much less likely to occur on a remote mountainside. Despite spatial homogeneity’s limitations, social scientists employ these statistical techniques carefully owing to their powerful explanatory utility. In light of these limitations, it must be cautioned that the and techniques were used in this study as a way to confirm preliminary results, but that these results must be interpreted cautiously.

That said, the is expressed as:

Equation 7 (Wimble et al., 2006)

Where:

is the point-event distance

is the event-event distance

= number of nearest neighbour points within w(x)

Interpreting the and is a relatively simple process. Visual inspection of the plot indicates whether clustering of the data is present when there is an excess of short distances between neighbours (MathSoft, 2000), whereas regularity, or randomness, within the data is evident when there is an excess of long distances between the neighbours (MathSoft, 2000). Visual illustration displays the cumulative density of the points (neighbours), and that distance is displayed on the x-axis (Wimble et al., 2006).

Interpreting the is done using directly opposing values; with , the excess of longer distances between values indicates clustering within the data

(MathSoft, 2000). After analyzing the point data visually, it is important to conduct a test of complete spatial randomness to determine if any clustering of data is occurring.

4.2.5.3 Nearest Neighbour

As the hypotheses in this study presumed that spatial clustering of both static and dynamic crime were evident, the null hypothesis then must assume the opposite, that there exists complete spatial randomness (i.e., no clustering of crime is evident). In order to establish this, many tests determine whether randomness is possible by comparing the actual crime distribution against a set significance level (Chainey, 2005). Two tests can be used to determine complete spatial randomness: nearest neighbour analysis (on point data) and spatial autocorrelation (on polygon data). As this study explored point and polygon level data, both tests for complete spatial randomness are included.

The nearest neighbour test is performed specifically on the point data.

This “compares the actual distribution of crime data against a dataset of the same sample size, with random distribution” (Chainey, Methods and techniques for understanding crime hot spots, 2005). This process calculates the distance from each point to its nearest-neighbour point. The sum of the distance for all points is then divided by the number of points in the data, providing us with a value representing the observed average nearest neighbour distance (Chainey,

2005).

A random distribution is then created within the same location, and an average distance is calculated between these ‘random’ locations (Chainey,

2005). The nearest-neighbour distance is then the ratio of the observed average distance between the observed points compared to the random (Chainey, 2005).

Equation 8 Nearest Neighbour Distance (Rogerson, 2001, 161)

Where:

= ratio

= mean distance of points from their nearest neighbour

= number of points per unit area

Generating the final results created a nearest neighbour index closer to 1.0, indicating a lack of clustering. Results that were less than 1.0 indicate that spatial clustering is more evident. In general, any result that falls closer to 0 indicates that spatial clustering is more evident, as 0 would indicate that all points are in exactly the same location) (Rogerson, 2001). This study utilized CrimeStat III, a spatial analysis software program designed by Ned Levine and associates (2004) at the National Institute of Justice. The nearest neighbour analysis was conducted with the defined neighbours of 50, no border correction, and a surface area of 114 kms. CrimeStat was also used to calculate the spatial autocorrelation of point data in addition to the nearest neighbour index.

4.2.5.4 Spatial Autocorrelation (SAC)

Spatial autocorrelation, as was previously noted, can be used on point or polygon data. The polygon data is discussed further in this chapter; however, the additional statistic was utilized on the point data to compare the value of the

variable at each location with the value at all other locations (Levine, 2004). The spatial autocorrelation is expressed as follows:

Equation 9 Moran’s I Statistic. Source: (Fortin et al., 2002, 5)

Where:

= elements of a weight matrix for which a value of 1 indicates a pair of

two samples, xi and xj = are in the distance class d, and a value of 0 indicates all of the other cases.

= the sum of

Interpreting the Moran’s I statistic is rather simple. A value nearing +1.0 indicates a strong spatial pattern, as high values tend to cluster with high, and low tend to cluster with low (Rogerson, 2001). Alternately, a value nearing -1.0 indicates a strong negative spatial autocorrelation wherein high values tend to be located near low (Rogerson, 2001). Following this calculation, spatial intensity plots were conducted to display cartographical representations using x and y plots.

4.2.5.5 Spatial Intensity Plots

S-Plus Spatial Statistics Software was used to create spatial intensity plots. The purpose of intensity plots is threefold. First, the intensity of a point pattern can be displayed through a contour plot. Secondly, the intensity of the point pattern mean can display a 3-D intensity graph of the aggregated point

estimates. Finally, the binning estimate method (as used in this study) illustrates the intensity locally over the total region, while returning a data frame containing smoothed intensity estimates (Levine, 2004). Specifically, “the binning method uses a two-dimensional histogram to form rectangular bins” (Kaluzny et al., 1998,

159). The counts in these bins are smoothed using a loess smoothing algorithm

(Kaluzny, et al., 1998). As a result, a surface plot of the spatial point pattern intensity is displayed graphically. After determining whether the data are clustered or spatially random, it is then important to determine the dispersion of the point data (as seen below), which can be evaluated using standard deviation ellipses (SDEs) (Levine N. , 2004).

4.2.5.6 Standard Deviational Ellipses (SDEs)

After determining whether the data are clustered or spatially random, it is then important to determine the dispersion of the point data, which can be evaluated using standard deviation ellipses (SDEs) (Levine N. , 2004).

Dispersion’s relevancy lies in its ability to demonstrate spatial and/or temporal changes or shifts in data. Standard deviational ellipses facilitate the comparison of both static (break-and-enter) and dynamic (assault) crime by examining the circularity produced from a visual depiction of observations on a two-dimensional surface around major and minor axes (Langworthy and Jeffris, 2000).

The utility of the SDE is based on the measurements produced from the coefficient of circularity (CC)3 which represents how much linearity there is within a distribution (Langworthy & Jefferis, 2000). Statistically, this SDE is calculated using a bivariate distribution defined by:

Equation 10 Standard Deviational Ellipse (Levine, 2004)

Thus the researcher must obtain the mean latitude (x) and the mean longitude

(y), the calculated area of the ellipse, the angle of rotation, as well as the transformed x’s and y’s and the coefficient of circularity (CC) 3 (Langworthy &

Jeffris, 2000).

Once this has been calculated, the distributions can be compared by analyzing the coefficient of circularity. A coefficient of circularity approaching 0.0 indicates a linear relationship, whereas a result approaching 1.0 indicates circularity within the point distribution (Langworthy & Jeffris, 2000). Mean centre is a simple descriptor of the distribution. It represents only the mean of the x and y coordinates (Levine, 2004). The formula for computing a mean centre is as follows:

Equation 11 Mean Centre Equation (Levine, 2004, 4.4)

Where:

and = the coordinates of individual locations

= total number of points

The standard deviational ellipses are also simple descriptors. The ellipse provides a single statistic which illustrates the dispersion in two dimensions on a map (Levine, 2004). The importance of the ellipse and the mean centre is to provide an accurate depiction of the dispersion of the data prior to conducting

Kriging interpolation tests. The reasons for this are twofold. First, it provides an overview of the data that can facilitate comparison (i.e., how distribution shifts over time or whether crime patterns change over months or years), but it also allows us to compare the two distributions (the model group 70% and the test group 30%) with the distribution of the total assault database in order to ensure that the data are reliable enough to use in further interpolation modelling such as

Kriging analysis.

For example, the total assault database was split using SPSS to randomly assign the data into either the test or the model group. In order to ensure the

spatial accuracy of the data, the model and test group may vary slightly, but they

should generally demonstrate a similar distribution to that of the full assault

dataset. If the datasets did not show a similar mean and dispersion, the process

would have had to be redone. Once spatial clustering and dispersion have been

evaluated, the final form of point data analysis was the interpolation of points

using Kriging, a geostatistical prediction technique discussed in Chapter 2.

4.2.5.7 Kriging

To understand Kriging, it is important to review the assumptions of spatial effects. As Calderon (2009) points out, spatial effects are defined as two types: spatial dependence (also known as spatial autocorrelation) and spatial heterogeneity. Spatial dependence indicates the existence of a functional relationship between two distinct spatial locations, while spatial heterogeneity assumes that the functional forms vary within locations and are not homogenous throughout a data set (Calderon, 2009).

Within the context of crime data, Environmental Criminology theories suggest both that crime is clustered and that spatial dependence may exist, thus several methods may be used to test for spatial dependence. Tests of spatial autocorrelation18 using Moran’s I19 are appropriate for areal or polygon level

data; these are discussed in the polygon data section that follows. Kernel

smoothing forms of interpolation are typically used as a point data alternative (as

18 Spatial autocorrelation refers to the value of a variable at a spatial location (i.e., a house break- and-enter) that is related to the value of the same variable in a nearby location (i.e., a house break-and-enter down the street) (Rogerson, 2001). 19 Moran’s I is a statistic that measures the degree of spatial autocorrelation found in areal data (Rogerson, 2001)

discussed in Chapter 2), however, an important objective of this thesis was to

demonstrate that a method called Kriging is just as useful, if not more so, than

the predictive and autocorrelative tests currently used. Specifically, Kernel

smoothing is similar to Kriging in that it estimates the values at a location by

using the input observations for that area. Kriging interpolates the values based

on a variogram while minimizing the variance. Kriging in this study utilized a

variation of the Kriging approach, different from Kernel smoothing, by replacing

the variogram with Georisk. Georisk was considered the average risk across all

locations in the study area as a fraction of one (Zizler, 2008).

The Kriging technique is considered an interpolation method from the

geostatistical family. Geostatistics “applies the theories of stochastic processes and statistical inference to geographic phenomena. It was traditionally used in geo-sciences” (Enlexica, 2009, 1). The Kriging technique, based on models of

autocorrelation, is employed specifically to assess the value of a random function

at an unobserved spatial location, given the observations of its neighbouring

location values (Calderon, 2009).

From this point, two forms of Kriging were possible. The most general

form used in this study was universal Kriging; it is typically utilized “when the

surface is estimated from irregularly distributed samples where trends exist (a

condition called nonstationarity)” (Demers, 2000, 272). The second form, known

as punctate Kriging, assumes that the data exhibits stationarity because it lacks a

trend (Demers, 2000). As the Environmental Criminology perspective of crime

assumes that crime tends to cluster in time and space and does not assume

stationarity or lack of trends, a variation of the universal Kriging was the most

appropriate method to use to interpolate criminal event data.

Equation 12 Kriging Estimator Function (Diggle et al., 1998, 299)

Where:

= the measured value at the ith location

= an unknown weight for the measured value at the ith location

= the prediction location

= the number of measured values

Several benefits stem from choosing Kriging over other methods. The most

valuable advantage to this study was that Kriging not only used autocorrelation

models, it also allowed for the production of a prediction surface that offers a

measure of the certainty or accuracy of the predictions (Soil and Water Research

Group, 2007). Throughout this study, Kriging was employed to assess the

distance or direction between sample points while reflecting a spatial correlation

which, in turn, was used to explain variations in the crime surfaces (Soil and

Water Research Group, 2007).

Specifically, Kriging in this study was a multi-step process used to explore both break-and-enter and assault spatial surfaces using variogram modelling; this, in turn, created a spatial surface that could be displayed in the form of a

map. Geographic Crime Risk Assessment Software was utilized to demonstrate variations of the current techniques using differing types of triangulation and wavelet techniques.

The basis for testing this hypothesis was that the Kriging technique has typically been used in fields such as health care and the environment. It has not been used to model crime data specifically; rather, similar techniques from the same family (e.g., kernel smoothing) were used. Despite not using this statistic, it was important to test its applicability to crime data to determine whether it might add value to the crime analysis process.

After consulting a mathematician, Peter Zizler of Mount Royal University, it was determined that it should not only be possible to utilize this technique for the assessment of crime data, but that new advancements could enhance the current techniques used in other software such as ArcGIS.

Therefore, a secondary aspect of this study was to assist in the development of the Geographical Crime Risk Assessment Software that uses the

Kriging technique to assess criminal event data. The software is discussed in more detail in Section 4.2.2 of this chapter, but in general terms, the software we developed interpolates crime data that are spatially scattered by the corresponding x and y coordinates. Once the data are imported into the program, a uniform grid is generated, and the software then provides the user with a crime risk assessment by displaying regions of high and low risk using the Kriging technique (Zizler, 2007).

This software offers two enhancements. First, it uses a form of Delaunay triangulation (a process that favours equilateral triangles and avoids skinny or fat triangles), and that is the first step toward capturing the collective effect of spatial crime locations (Zizler, 2007). After selecting and fixing a threshold for the size of the triangle areas, a zero function value is then placed in the centroid of the triangle (Zizler, 2007). The data are then re-triangulated until all the triangle areas in the triangulation fall below a given threshold (Zizler, 2007).

The second beneficial enhancement is the uniform grid which allows the wavelet low pass filter to process the data several times. That grid is then overlaid on the data to provide a crime risk surface visual display (Zizler, 2007).

The final product allows the user to locate the boundaries of those regions with a high or low crime risk association.

The objective of this study was to create more robust and predictive crime analysis models for static and dynamic crime analysis. However, when examining predictive techniques like Kriging, it is still necessary to explore and describe the data in multiple ways to provide substantive analysis and description of the phenomenon studied. Even though local data analysis and predictive modelling was conducted, global analysis, or polygon level data analysis, was also essential as it provides additional information about the models created.

Consequently, for the purpose of this study, the following section outlines the basic descriptive analysis and spatial autocorrelative test conducted. Both forms of analysis are descriptive and exploratory, but they offer a different

perspective of the data from the analysis conducted in point/local levels of analysis.

4.2.6 Polygon Data

4.2.6.1 Descriptive

Descriptive analysis of polygon data included the use of several key census data variables in order to display the data within the neighbourhood boundaries. For example, the levels of income for each neighbourhood can be illustrated among the geographic census boundaries and then cartographically displayed. Descriptive analysis was conducted for informative purposes only, as it provides context and understanding of the demographic and land make-up of the city of Regina, Saskatchewan.

4.2.6.2 Neighbours

The next phase of analysis was to conduct spatial autocorrelative tests.

However, in order to conduct this form of analysis, it is important to define neighbours at the polygon level so that autocorrelation can be done. Polygon level tests require that neighbours be defined. For example, polygon level analysis like spatial autocorrelation bases its statistics on point data that has been aggregated to a polygon boundary level. Defining neighbours is a spatial process “modelled by predicting the outcome of each region based partially on its dependence on nearby or neighbouring regions” (Kaluzny et al., 1998, 111).

Because crime locations are aggregated to a polygon level, it was essential to

define neighbours in order to be able to conduct any form of spatial analysis on the areal data.

The calculation used to define spatial neighbours in this study used the

Regina neighbourhood census boundary data from 2005. Neighbours were defined by the first order neighbour method because the neighbour calculations were based on the juxtaposition of a neighbourhood boundary bordering on another neighbourhood boundary (Griffith, 1987; Thompson, 2003). After the first order neighbour file was created, it was then used in ArcGIS to define the neighbourhood boundaries in order to conduct spatial autocorrelation.

4.2.6.3 Spatial Autocorrelation

Correlation tests are extremely common in most empirical studies in the social sciences. They are used to determine whether there is a relationship between two variables that is statistically significant beyond the level of chance variation. Two of the most common correlative tests used are chi square (non- probabilistic) and Pearson’s r (probabilistic). Statistical tests like these measure a linear relationship between two variables, assuming that the observations of x and y are independent (Rogerson, 2001). The assumption that x and y are independent becomes a problem when applying variables from spatial locations

(Rogerson, 2001). As many note, “spatial data often exhibit dependence”

(Rogerson, 2001, 98). This spatial dependence is the likelihood that data may be either spatially clustered or spatially dependent on their neighbours.

Several different tests for the existence of spatial correlation can be used: the residual join count statistic; Moran’s I; and Geary’s C. Although each of these

tests have benefits, drawbacks include the fact that the count statistic utilizes a matrix of positive and negative residuals to indicate where clustering on a map occurs (Rogerson, 2001). This presents a problem when spatial autocorrelation is signified using positive and negative signs that do not account for magnitude

(Rogerson, 2001), as it was in this case.

For this study, Moran’s I statistic was preferred because it is one of the most commonly applied methods and it has previously been used to test for evidence of criminal event clustering (Chakravorty, 1995). Moran’s I is considered a significance test that creates an estimate of the standard error of the autocorrelation coefficient by randomly permuting the x variable across the spatial zones and calculating an autocorrelation coefficient for each permutation run (Fotheringham et al., 2000). With an adequately large number of

autocorrelation coefficients, we can produce an experimental distribution that

allows statistical inferences to be made regarding the observed autocorrelation

coefficient (Fotheringham et al., 2000).

Moran’s I statistic is computed by comparing the value at any one location

with values at all other locations (Levine, 2002; Bailey & Gatrell, 1995; Anselin,

1995; Ebdon, 1985). Specifically, Moran’s I uses an intensity value (weighting) to measure the spatial proximity between regions, and the addition of measuring distance is a key component of this analysis. The spatial weighting may be expressed “as simple contiguity (having a common border), distance contiguity

(having centroids within the critical distance band), or in a function of inverse

distance or squared inverse distance” (Anselin 1992, as quoted by Chakrovorty &

Pelfrey Jr., 2000, 69). Accordingly, Moran’s I is represented as:

Equation 13 Moran’s I Statistic. Source: (Fortin et al., 2002, 5)

Where:

= elements of a weight matrix for which a value of 1 indicates a pair of

two samples, and xj = are in the distance class d, and a value of 0 indicates all of the other cases

= the sum of

Interpreting the Moran’s I statistic is rather straightforward, using the same process as spatial autocorrelation for point data. A value nearing +1.0 indicates a strong spatial pattern as high values tend to cluster with high, and low tend to cluster with low (Rogerson, 2001). Alternately, a value nearing -1.0 indicates a strong negative spatial autocorrelation where high values tend to be located near low (Rogerson, 2001).

In this study, observations were aggregated to a neighbourhood census boundary. Therefore, the Moran’s I represented the observations in each neighbourhood and accounted for the spatial proximity of break-and-enter and assault cases between neighbourhood boundaries.

4.2.7 Summary

It is clear from the information above that there are many statistical techniques that can and have been used to create spatial analyses of crime. This particular study is rather unique in that it:

a) utilized two different types of data to compare models (i.e., static

and dynamic crime);

b) utilized new software to test these models;

c) utilized geostatistics, specifically Kriging, to create the models;

and finally,

d) an extremely thorough examination of the data was conducted

utilizing a combination of point and polygon data analysis

techniques while finalizing the predictive model with

geostatistical comparisons, rather than creating a model using

only one or two statistics.

A detailed analysis of the data below comprises the final section of this case study; results are discussed in three main sections: 1) Point data results of assault and break-and-enter; 2) Polygon data analysis of assault and break-and- enter; and 3) Comparative results of both models.

4.3 Results

Crime location prediction is a different concept in this study as it basically uses a combination of traditional techniques based on the Geography of Crime to describe and predict a particular model of interest. Such techniques should more

accurately predict crime locations for offence types involving static targets (such

as break-and-enter) than they would offences involving mobile targets (such as assault), given that the latter’s positions are dynamic and thus more difficult to predict. It was therefore hypothesized that crime prediction should not only be appropriate, but also more accurate, when applied to break-and-enter (as houses and buildings are static structures), rather than to assault (as people are generally more mobile, a factor that makes prediction more difficult).

The results of this hypothesis are discussed below. Due to the complexity of this study, they are presented in several sections that include: point data results for assault, point data results for break-and-enter, polygon data results for assault, and polygon data results for break-and-enter. The final section offers an overview of the comparison between both break-and-enter and assault.

4.4 Point Data Results

As discussed in section 4.2, two forms of data analysis, point and polygon,

were conducted during this study. Point data analysis uses statistics to analyze

crime based on single x and y coordinates for each criminal incident, whereas

polygon-level data analysis uses the locations of criminal activities aggregated to

a neighbourhood boundary level. Both forms of data analysis were conducted on

assault (dynamic crime) and on break-and-enter (static crime).

4.4.1 Assault Point Data Results

4.4.1.1 Assault Temporal Results

Initial assessment of the point data began with a temporal analysis of

patterns or trends. The results depicted in Figure 5 of assaults by time of day in

Regina illustrate several interesting patterns.

Figure 5 Total Assault in Regina 2005, by the Hour Total Assaults by Hour in Regina 2005 140 120 100 80 60 40 Total Number of of Number Assaults 20 0 22:00) 02:00) 03:00) 04:00) 05:00) 06:00) 07:00) 08:00) 09:00) 10:00) 11:00) 12:00) 13:00) 14:00) 15:00) 16:00) 17:00) 18:00) 19:00) 20:00) 21:00) 24:00) 01:00) 23:00) ------(01:00 (01:00 (02:00 (03:00 (04:00 (05:00 (06:00 (07:00 (08:00 (09:00 (10:00 (11:00 (12:00 (13:00 (14:00 (15:00 (16:00 (17:00 (18:00 (19:00 (20:00 (23:00 (00:00 (00:00 (21:00 (22:00

The initial inspection illustrates that the highest concentration of assaults by the

hour occurs between 9:00 pm and 10:00 pm (n = 129). The second highest cluster happens between 6:00 pm and 7:00 pm (n = 119), whereas the most

infrequent number of assaults taking place in Regina is between 6:00 am and

7:00 am (n = 37).

However, an interesting pattern is being temporally created from a visual

inspection; the majority of assaults occur in two clusters, the first from 2:00 pm to

7:00 pm (n = 573) and the second from 9:00 pm to 4:00 am (n = 744). Consistent

with previous research, we would typically expect to see an increase in the

number of assaults later at night owing to the timely and cumulative effect of bars

closing along with the general effects of the alcohol and drug subculture.

However, the pattern from 2:00 pm to 7:00 pm is worthy of note, and possible

explanations (e.g., happy hour) are discussed in Chapter 5. Nevertheless, it is an interesting pattern that indicates a very high incident level of assault throughout the majority of the afternoon, evening, and early morning.

4.4.1.2 Complete Spatial Randomness (CSR)

Prior to conducting further statistical analysis, it was important to test the

original data for complete spatial randomness (CSR). Two common assumptions

determine whether a point pattern is random; the first is that the intensity of the pattern will not vary over the region, and the second is that there be no interactions evident among them (i.e., autocorrelation) (MathSoft, 2000).

In regard to the assault database, the and the were conducted on the

entire database (n = 2,197) to determine whether a preliminary visual inspection

found clustering or randomness of assaults. As Figure 6 illustrates, the shows

an excess of short distances between neighbours, and the demonstrates an

excess of longer distances between neighbours. These results indicate that we

would expect to see upon initial inspection that assaults are not completely

spatially random and that patterning does in fact occur.

Figure 6 Complete Spatial Randomness of Assault Data

4.4.1.3 Nearest Neighbour Index (nna)

After determining that the assault data visually presents clustering of crime locations, the next stage of spatial analysis was to conduct nearest neighbour index analysis (nna) using CrimeStat software. The nearest neighbour index is a relatively simple tool, as well as being one of the oldest distance tools used to understand and calculate neighbour distance (Levine, 2004).

Turning now to an examination of the dynamic crime of assault in Regina in 2005, there were 2,197 assault incidents over the course of the entire year.

The area of Regina is 3,408 square kilometres, or approximately 1,316 square

miles. Table 3 illustrates the nearest neighbour statistics for three separate

databases, a) the assault total (100%, all incidents), b) the assault model (70%)

and c) the assault test group (30%). It was crucial to test all three databases to

ensure that both the model and the test group effectively depicted the same

patterning we expected to see in the total assault file.

Table 3 Nearest Neighbour Results for Assault

Nearest Neighbour Statistics for Assault

Assault Assault Assault Total 100% Model 70% Test 30% Mean Nearest Neighbour 0.043 mi 0.05 mi 0.076 mi Distance Mean Random Distance 0.094 mi 0.108 mi 0.145 mi

Nearest Neighbour 0.453 0.46 0.526 Index Standard Error 0.001 mi 0.002 mi 0.003 mi

Test Statistic (Z-Score) -41.308 -35.415 -21.48

P-value 0.000 0.001 0.000

As outlined in Table 3, in regard to the total assault incidents dataset, the

mean nearest neighbour distance was 0.043 miles, while the mean nearest neighbour random distance expected was 0.094 miles. The nearest neighbour index was therefore 0.453 with a Z-value of -41.308. These results were highly

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significant (p < 0.01), indicating that the nearest neighbour distances of assaults in Regina were shorter than we would expect if the results were random.

In regard to the assault model 70% group, the mean nearest neighbour distance was 0.05 miles, while the mean nearest neighbour random distance expected was 0.108 miles. The nearest neighbour index was therefore 0.46 with a Z-value of -35.415.20 These results were highly significant (p < 0.01) and again indicate that the nearest neighbour distances of the assault model group in

Regina were shorter than we would expect if the results were random.

Finally, with the assault test 30% group, the mean nearest neighbour distance was 0.076 miles, while the mean nearest neighbour random distance expected was 0.144 miles. The nearest neighbour index was therefore 0.526 with a Z-value of -21.48. These results were highly significant (p < 0.01) and indicated that the nearest neighbour distances of the assault test group in Regina were shorter than we would expect with random results. Figure 7 delineates the nearest neighbour analysis in ArcGIS, thus confirming the spatial clustering in the data.

20 Note: The Z-value for the model and test group will be smaller than that of the full assault database owing to the nature of the decreased sample sizes.

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Figure 7 Nearest Neighbour Analysis of Assault

As discussed earlier in this chapter, interpreting the Moran’s I statistic is rather simple. A value nearing +1.0 indicates a strong spatial pattern, as high values tend to cluster with high and low tend to cluster with low (Rogerson,

2001). Alternately, a value nearing -1.0 indicates a strong negative spatial autocorrelation wherein high values tend to be located near low (Rogerson,

2001).

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Table 4 Spatial Autocorrelation of Point Data for Assault in Regina 2005

Spatial Autocorrelation of Assault Point Data Evidence Moran’s I Z-Value P-Value of Clustering Assault Total Group -0.009 -3.798 0.000 Yes 100% Assault Model Group -0.010 -3.212 0.001 Yes 70% Assault Test Group -0.012 -1.715 0.05 Yes 30%

As illustrated in Table 4, significant clustering existed in all three databases.

However, none of these determined a strong spatial autocorrelation on the point data. It was therefore important to examine the data more closely by using intensity and visual data plots prior to conducting interpolation techniques such as Kriging.

4.4.1.4 Intensity and Surface Plots

The next stage of analysis conducted was intensity and surface plots. As

Figure 8 indicates, the contour plot illustrates a very tight point pattern intensity

with contours very close together. The surface plot located to the right of the

contour plot, then, illustrates only a large intensity of assault. This pattern

seemed to reflect an extremely high concentration of assaults at the centre of the

city along with a slight dispersion throughout the rest of Regina. The final filled

contour plot illustrated the tight intensity of assault clustering which indicates a

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low level of dispersion, a high level of clustering, and two large hotspots, both located in north central Regina.

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Figure 8 Intensity and Surface Assault Plots

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Despite knowing that the data were not spatially random, that clustering is evident, that neighbours are spatially located near one another, and that the

intensity of the cluster seems to be at the centre of the city (as depicted in Figure

8 above), it was nonetheless important to conduct further testing. The intent of

the next phase was simply to visually examine the patterning of the data.

When we did so (see Figure 9 below), it was evident that several issues

should be discussed. First, the data were displayed in both polygon (boundary

intensity of aggregated point data) and point format (intensity by the size of the

point on the map). From that illustration, it was evident that the highest

concentration of crime, as indicated in the intensity plots, was located at the city

centre in downtown Regina. A secondary concentration bordered the downtown

north central area of the city.

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Figure 9 Assault Total Incidents in Regina 2005

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4.4.1.5 Standard Deviational Ellipses and Mean Centre Analysis

Analyzing both the standard deviational ellipses and the mean centres of the point data was the final, vital form of analysis required prior to conducting

Kriging interpolation methods. Table 5 depicts the statistical results for the mean centre. The x and y coordinates of the total assault dataset were relatively similar to that of the model and test groups, indicating that there was little relative difference in the means of all three groups.

Table 5 Mean Centre Assault Results

Mean Centre Assault Results

Dataset M X M Y SD X SD Y

Assault Total 100% -104.614090 50.455811 0.026441 0.015349

Assault Model 70% -104.614019 50.455468 0.026389 0.015453

Assault Test 30% -104.614261 50.456650 0.026589 0.015073

The length and area of the standard deviational ellipses illustrated in Table 6 also depicted an extremely similar result.

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Table 6 Length and Area of Standard Deviational Ellipses for Assault Length and Area of Standard Deviational Ellipses

Data Set Y Axis Length X Axis Length Area of Ellipse

Assault Total 100% 2.534 mi 3.659 mi 7.281 sq mi

Assault Model 70% 2.581 mi 3.637 mi 7.373 sq mi

Assault Test 30% 2.415 mi 3.715 mi 7.045 sq mi

Graphically, the results from the tables above were then displayed spatially.

Figure 10 outlines the mean centres and standard deviational ellipses for all three databases. The results indicated that the model and test group databases were consistent with the total assault database and could therefore be reliably used in a Kriging model.

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Figure 10 Standard Deviational Ellipses for All Assault Data

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4.4.1.6 Kriging

Following the exploratory point data analysis, the final step in the process was to model the data using the Kriging technique. As discussed, the objective of this study was primarily to determine whether Kriging could be used to create a geostatistical risk surface of crime data, and if so, it was proposed that it would probably be more effective in the analysis of static crime such as break-and-enter than it would for dynamic crime like assault.

The assault dataset was first tested by applying the Kriging method to the model group (70%). If the technique successfully created a geographical risk surface,21 we would expect to see a similar Georisk22 and a cumulative Georisk23 correlating with the original model group in the test data group (30%). Figure 11 depicts the initial overview of the assault model and the test groups before the

Georisk surface was applied.

21 Geographical risk surface is comprised of a rectangular grid displaying the Georisk in the study area. It is displayed as a colour image, where red shading indicates a high risk area and blue means a low risk area (Zizler, 2008). 22 Georisk is defined “as the average risk over all locations in the city as a fraction of one, the risk assessed at P” (Zizler P. , 2008, p. 1). 23 Cumulative Georisk is defined as the average perceived risk over all locations in the city when many (not just one) crime events previously took place.

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Figure 11 Assault 70% and 30% Point

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Visual inspection of the data illustrated similar patterning of the model and test group data. Despite this initial visualization, the similarity was still only an assumption, thus further analysis was necessary. The first step was to apply

Delaunay triangulation to both sets of x and y coordinate data. A visual example of that triangulation is depicted in Figure 12.

Figure 12 Assault Model Triangulation

After triangulating the data, a Georisk surface was calculated and overlaid on the point data for each dataset, displayed in Figure 13.

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Figure 13 Assault Kriging Clusters

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Finally, after calculating that initial risk surface, the mesh (grid) was then refined with several iterations (two is the typical default number) (Zizler, 2007).

Throughout the refining process, the software was smoothing the risk surface by applying numerous wavelet iterations in order to assess the clustering of the data

(Zizler, 2007). The final product (see Figure 14) was a smoothed Kriging surface illustrating the Georisk within Regina for assault in 2005.

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Figure 14 Assault Smoothed Kriging Surfaces

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The output of the Georisk smoothed surface displayed those areas that were statistically deemed a high risk for a repeat assault to occur. Comparing the difference between the assault model group and the test group, it was apparent that the objective of this study was correct. It did create an accurate portrayal of where one would expect a predictive surface to illustrate a high risk area based on all the other tests done prior to Kriging.

Even more interesting, though, is that a principal assumption of this study was that the Kriging would not work as well for dynamic crimes like assault owing to the mobility factor. Therefore, a correlative test was conducted using the

Kriging procedures in order to determine whether the model and the test group were correlated, and whether the results successfully predicted criminal activity occurring in the locations specified by the software.

In calculating the correlations between the model and the test group, the risk mean was 0.127 with a standard deviation of 0.218. The correlation coefficient was 0.613 with a Z-Score of 2.233, indicating that the model and the test group were highly correlated, as depicted in Figure 15. Interestingly, though assault was considered the dynamic (mobile) crime, we have to consider that there may be an element of stationarity (i.e., assaults occurring at or near stationary locations such as drinking establishments, parks, low income housing areas, etc.), a finding discussed in the following chapter.

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Figure 15 Assault Model and Test Group Kriging Correlation

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4.4.2 Break-and-Enter Point Data Results

4.4.2.1 Break-and-Enter Temporal Results

Preliminary assessment of the break-and-enter point data was performed through temporal analysis of trends and patterns. Examination of the results in

Figure 16 of break-and-enter by time of day in Regina in 2005 demonstrated some agreement with the literature, but there were also some contrary patterns.

Figure 16 Total Break-and-Enters by the Hour in Regina, 2005 Total Break & Enters by Hour in Regina 2005 180 160 140 120 100 80 60 40 Total 20 0 02:00) 03:00) 04:00) 05:00) 06:00) 07:00) 08:00) 09:00) 10:00) 11:00) 12:00) 13:00) 14:00) 15:00) 16:00) 17:00) 18:00) 19:00) 20:00) 21:00) 22:00) 23:00) 24:00) 01:00) ------(01:00 (01:00 (02:00 (03:00 (04:00 (05:00 (06:00 (07:00 (08:00 (09:00 (10:00 (11:00 (12:00 (13:00 (14:00 (15:00 (16:00 (17:00 (18:00 (19:00 (20:00 (21:00 (22:00 (23:00 (00:00 (00:00

For example, some research indicates that the most frequent burglaries

occurred between the hours of 3 pm and 9 pm during the first part of the week

(i.e., Monday through Thursday). However, the pattern was different for Friday

through Sunday; on those days, the frequency was higher from 9 pm to 3 am.

Unfortunately, the nature of the data available to this study meant that

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information about the day of the week was not available by the hour. However,

an examination of the chart in Figure 25 illustrated that there was no distinct,

overall pattern. Rather, it reflected a high concentration of reported break-and-

enters occurring between 9 am and midnight (n = 1,658). The highest spike

occurred from 4:00 pm to 5 pm (n = 154), while the lowest occurrence of break-

and-enters occurred between 5:00 am and 6:00 am (n = 15). Despite a large

amount of research, it was difficult to determine distinct time patterns from this data. Separation by day of the week may well have clarified the analysis.

4.4.2.2 Complete Spatial Randomness (CSR)

As discussed in the point data assault analysis, it was important to test the

original data for complete spatial randomness (CSR). The two techniques used

to determine whether it exists for break-and-enters include the and the . Their interpretation follows the same process outlined earlier with respect to the assault data. By visually inspecting the plot, we can see whether clustering of the data is present when there is an excess of short distances between neighbours (MathSoft, 2000), whereas regularity, or randomness, within the data is evident when there is an excess of long distances between the neighbours

(MathSoft, 2000). Interpretation for the was exactly the opposite of the , in

that the excess of higher distances between values indicated clustering within the

data (MathSoft, 2000).

With the break-and-enter database, the and the were conducted using a preliminary visual inspection on the entire database (n = 1,875) to determine

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whether clustering or randomness of break-and-enters occurred. Figure 17

illustrates the results; The showed an excess of short distances between neighbours, while the demonstrated an excess of longer distances between

neighbours. Upon initial inspection, these results indicated that break-and-enters are not completely spatially random, and that patterning did, in fact, exist among the crime locations.

Figure 17 Complete Spatial Randomness for Break-and-Enters

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4.4.2.3 Nearest Neighbour Analysis (Nna) and Autocorrelation

After determining that the break-and-enter data visually presented clustering of the crime locations, the next stage of spatial analysis, similar to the process delineated for the assault analysis, was to conduct nearest neighbour index analysis (nna) using the CrimeStat software.

As was discussed previously, the nearest neighbour index is a relatively simple tool, as well as being one of the oldest distance tools used to understand and calculate neighbour distance (Levine, 2004). The nearest neighbour index uses the distances between the nearest points (crime locations) and compares it to the distances that we would expect to see if the relationship were based entirely on chance (Levine, 2004).

Regarding the static crime of break-and-enter in Regina in 2005, there

were 1,875 break-and-enter incidents for the entire year. The area of Regina is

3,408 square kilometres, or approximately 1,316 square miles. Table 7 illustrates

the nearest neighbour statistics for three separate databases: a) break-and-enter

total (100%, all incidents); b) break-and-enter model (70%); and c) break-and-

enter test (30%).

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Table 7 Nearest Neighbour Statistics for Break-and-Enter

Nearest Neighbour Statistics for Break-and-Enter

B-&-E Total B-&-E Model B-&-E Test

100% 70% 30% Mean Nearest Neighbour 0.040 mi 0.05 mi 0.079 mi Distance Mean Random Distance 0.09 mi 0.106 mi 0.15 mi

Nearest Neighbour Index 0.452 0.462 0.525

Standard Error 0.001 mi 0.002 mi 0.003 mi

Test Statistic (Z) -43.417 -35.89 -21.643

P-value 0.000 0.001 0.000

For the total break-and-enter dataset, Table 7 reported that the mean nearest

neighbour distance was 0.040 miles, while the mean nearest neighbour random

distance expected was 0.09 miles. The nearest neighbour index was therefore

0.452 with a Z-value of -43.417. These results were highly significant (p < 0.01),

indicating that the nearest neighbour distances of break-and-enter in Regina

were shorter than would be expected if the results were random.

Results for the break-and-enter model 70% group were that the mean

nearest neighbour distance was 0.049 miles, while the mean nearest neighbour

random distance expected was 0.106 miles. The nearest neighbour index was

therefore 0.462 with a Z-value of -35.89.24 These results were highly significant

(p < 0.01), indicating that the nearest neighbour distances of the break-and-enter

24 Note: The Z-value for the model and test group will be smaller than that of the full break-and- enter database owing to the nature of the decreased sample sizes.

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model group in Regina were again shorter than we would expect were the results random.

Finally, when we examined the assault test 30% group, the mean nearest neighbour distance was 0.079 miles, while the mean nearest neighbour random distance expected was 0.15 miles. The nearest neighbour index was therefore

0.525 with a Z-value of -21.643. These results were again highly significant (p <

0.01), indicating that the nearest neighbour distances of the break-and-enter test group in Regina were shorter than random results would produce. Figure 18 showed that the nearest neighbour analysis in ArcGIS confirms the spatial clustering in the data.

Figure 18 Nearest Neighbour Results for Break-and-Enter

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CrimeStat was also used to calculate the spatial autocorrelation of point data in addition to the nearest neighbour index. Spatial autocorrelation, as discussed prior, can be used on point or polygon data. Interpreting the Moran’s I statistic is rather simple. A value nearing +1.0 indicates a strong spatial pattern, as high values tend to cluster with high and low tend to cluster with low

(Rogerson, 2001). Alternately, a value nearing -1.0 indicates a strong negative spatial autocorrelation, one where high values tend to be located near low

(Rogerson, 2001).

Table 8 Spatial Autocorrelation of Break-and-Enter Point Data Spatial Autocorrelation of Break-and-Enter Point Data

Evidence Moran’s Z-Value P-Value of I Clustering B & E Total Group 0.004 2.035 P = 0.05 Yes 100% B & E Model Group 0.004 1.738 P = 0.05 Yes 70% B & E Test Group -0.0002 0.308 n.s No 30%

Table 8 indicates that significant clustering existed in two of the three databases.

However, similar to the assault databases results, these statistics did not show a strong spatial autocorrelation on the point data. It was therefore important to examine the data more closely by using intensity and visual data plots prior to conducting interpolation techniques such as Kriging.

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4.4.2.4 Intensity and Surface Plots

Intensity and surface plots for break-and-enters in Regina with graphs

created by S-Plus Spatial Statistics Software using the same binning techniques

used in the assault analysis was then conducted. As Figure 19 indicates, the contour plot reflected a very tight, intense point pattern with contours that were especially close together. The surface plot located to the right of the contour plot, however, illustrated only one large block, thus indicating numerous break-and-

enters. This pattern seemed to reflect an extremely high concentration of break- and-enters at the centre of the city, with a slight dispersion throughout the rest of

Regina. The final filled contour plot illustrated the tight intensity of assault

clustering that indicates a low level of dispersion, a high level of clustering, and a

large hotspot located in Regina’s inner city. This result was almost identical to the

outcome achieved when we worked with the assault data, indicating that this

inner city neighbourhood constituted a major problem area

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Figure 19 Break-and-Enter Intensity Plots

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With the knowledge that the data was not spatially random, that clustering was apparent, that spatial neighbours were close, and that the intensity of the cluster seemed to be at the centre of the city (as was also the case for the assault data), this data was tested further in order to visually examine the spatial patterning of the data in more detail.

The following map (Figure 20) is a cartographical representation of break- and-enter data in both polygon (boundary intensity of aggregated point data) and point format (intensity by the size of the point on the map). It was evident in this depiction as well as in the intensity plots that the highest concentration of crime occurred near Regina’s city centre in the downtown area.

As with assault, break-and-enters were largely concentrated around the city centre. Contrary to the assault locations, however, break-and-enters tended to disperse more into the surrounding communities; three secondary concentrations border the downtown area directly south, southeast, and southwest of the city centre.

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Figure 20 Break-and-Enter Total Incidents

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4.4.2.5 Standard Deviational Ellipses and Mean Centre Analysis

One final important step remained prior to applying Kriging interpolation

methods. It was necessary to examine standard deviational ellipses and mean

centres of point data. As discussed in the assault data analysis section, the mean

centre was a simple descriptor of the distribution explicitly representing the mean

of the x and y coordinates (Levine, 2004). The standard deviational ellipses were also simple descriptors in that they provided a single statistic illustrating dispersion on a map in two dimensions (Levine, 2004). Both the ellipse and the mean centre provided a visual and statistical depiction of the dispersion of the data prior to conducting Kriging interpolation tests.

Table 9 outlined the statistical interpretation of the mean centre for the x and y coordinates of the total break-and-enter dataset. The mean centre and standard deviational ellipses in Table 9 were similar to those of the break-and- enter model and test groups, indicating that there was a relatively minor difference in the means of all three groups.

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Table 9 Mean Centre Break-and-Enter Results

Mean Centre Break-and-Enter Results

Dataset M X M Y SD X SD Y

B & E Total 100% -104.617793 50.454208 0.027443 0.016020

B & E Model 70% -104.618193 50.454310 0.027448 0.016160

B & E Test 30% -104.616907 50.453984 0.027434 0.015718

Statistically, the length and area of the standard deviational ellipses, as illustrated

in Table 10, showed a very similar result with only minor deviations in length and area.

Table 10 Length and Area of Standard Deviational Ellipses for Break-and-Enters

Length and Area of Standard Deviational Ellipses Area of Dataset Y Axis Length X Axis Length Ellipse

B & E Total 100% 2.384 mi 3.97 mi 7.433 sq mi

B & E Model 70% 2.359 mi 4.008 mi 7.426 sq mi

B & E Test 30% 2.438 mi 3.893 mi 7.455 sq mi

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Graphically, the results from tables 9 and 10 were then presented cartographically. The illustration in Figure 21 demonstrated the mean centres and standard deviational ellipses for all three databases. The results indicated that the break-and-enter model and test group databases were consistent with the total break-and-enter dataset and could therefore be reliably used in a Kriging model.

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Figure 21 Break-and-Enter Standard Deviational Ellipses

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4.4.2.6 Kriging

Following the exploratory point data analysis of the break-and-enter data, the next phase was to model the data using the Kriging techniques. The assault data was the first dataset tested during this study. The surprisingly high correlation between the model and test group risk surfaces demonstrated the success of the technique; thus the Kriging method was applied to the break-and-

enter model group (70%). If the technique again successfully created a

geographical risk surface,25 we would expect to see a similar26 and a

cumulative27 Georisk in the test data group (30%) correlating with the original

model group, as happened with the assault results. Figure 22 depicts the initial

overview of the break-and-enter model and test group point data prior to

conducting the Georisk surface.

25 Geographical Risk Surface was a rectangular grid displaying the Georisk in a given study area (i.e., a city) (Zizler P. , 2008). It was displayed as a colour image where red means high risk and blue means low risk (Zizler P. , 2008). 26 Georisk was defined “as the average risk over all locations in the city as a fraction of one, the risk assessed at P” (Zizler P. , 2008, p. 1). 27 Cumulative Georisk was defined as the average perceived risk over all locations in the city when many (not just one) crime events previously took place.

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Figure 22 Kriging Break-and-Enter Point Data

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The break-and-enter point data illustrated similar patterning of both the

model and test group data. As mentioned previously, despite the initial visual

analysis, the clustering and risk could only be assumed until further analysis provided a risk prediction surface. The Geographical Crime Risk Assessment

Software was then used to compute the Delaunay triangulation on both sets of x

and y coordinates in the model and test group data. The resultant visual example

of break-and-enter triangulation was depicted in Figure 23.

Figure 23 Break-and-Enter Kriging Triangulation

After triangulating the break-and-enter data, the Georisk surface was calculated

and overlaid on the point data for each dataset (see Figure 24).

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Figure 24 Break-and-Enter Kriging Clusters

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Following the calculation of the preliminary risk surface, the mesh (grid)

was then refined using two iterations. As discussed earlier, during the refining

process, the software smoothened the risk surface by applying numerous wavelet iterations that allowed us to better assess the clustering of the data

(Zizler, 2007). The final smoothed Kriging surface depicting the Georisk within

Regina for break-and-enters in 2005 was evident in Figure 25.

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Figure 25 Break-and-Enter Smoothed Kriging Surfaces

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As with the assault data results, the Georisk smoothed surface displayed

those areas statistically deemed to be high risk for repeated break-and-enters to

occur. Based once again on all the other tests calculated prior to Kriging, the

assessment of the difference between the break-and-enter model group and the

test group initially indicated that the data displayed an accurate portrayal of

where we would expect the high risk areas to be.

A correlation test was then conducted using the Kriging process to

determine whether the break-and-enter model and test group were correlated

and whether the results successfully created a prediction risk surface of break- and-enters in Regina.

In calculating the correlations between the model and test group, the risk mean was 0.146 with a standard deviation of 0.233. The correlation coefficient was 0.551 with a Z-Score of 1.74, thus indicating that the model and test group were significantly correlated (see Figure 26).

Interestingly, the original hypothesis of this study purported that Kriging, if successful, would better predict static crime (such as assault) than it would dynamic crime (such as break-and-enter). However, as discussed in the following chapter, though both results were significant, the assault (static crime) tests actually demonstrated a higher significance and a stronger relationship between the model and the test group risk surface prediction than did the break-and-enter group, as indicated by Figure 26.

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Figure 26 Break-and-Enter Kriging Correlation

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4.5 Polygon Data Results

Despite having conducted very detailed point data analysis on the assault and break-and-enter data, polygon data analysis was still considered the final step in the process. The point data analysis demonstrated clustering of the data, and Kriging was able to be used for not only the break-and-enter analysis (as originally thought) but also for the assault analysis. Despite this, a more robust model could add polygon analysis to the process. This additional step could not only look for clustering, it might also indicate whether a) the data were dependent on its neighbours and b) whether something might be happening at a more aggregated neighbourhood level that was not evident at a point pattern level.

4.5.1 Assault Data Polygon Results

When conducting polygon data analysis, the point locations (i.e., assault locations) were aggregated to a neighbourhood boundary level. The aggregated data (intensity) was then cartographically displayed. In Table 11, the total (n =

2,197) assault rates for each neighbourhood in Regina in 2005 were displayed.

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Table 11 Assault Counts by Neighbourhood in Regina 2005 Assault Rates /1000 in Regina 2005, by Neighbourhood

Neighbourhood # of Neighbourhood # of Assaults Assaults

Arcola East 0.7 Dieppe 14.9

Prairie View 3.3 Glencairn *na

Twin Lakes 1.8 Glenelm *na Walsh Acres- Lakeridge 2.0 Core Group *na

Coronation Park 15.7 Al Ritchie 18.3 Argyle Park- Englewood 4.5 Lakeview 3.5

TBD5 *na Albert Park 2.7

Uplands 3.8 TBD2 *na

Northeast 17.1 Hillsdale 2.2

North Central 53.1 Gladmer Park 4.2

Regent Park 9.8 Boothill 2.6

Normanview 8.4 Normanview West 1.6 Rosemont-Mount Royal 5.9 Eastview 38.5

TBD1 *na Transitional Area *na

Downtown 619.5 Sherwood-McCarthy 3.2

Cathedral Area 10.4 Whitmore Park 3.9

McNab 13.0 Total n = 2,197 *Note: Some neighbourhood populations were unavailable due to industrial, transitioning and new emerging neighbourhoods prior to census collection. The total crime count includes neighbourhoods where populations were unavailable.

A preliminary look at the neighbourhood data indicated that the highest concentrations of assault by neighbourhood were located in the North Central neighbourhood with a rate of 53.1 assaults per 1,000 population (n = 493) on the

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north border of Downtown, and in the downtown area with a rate of 619.5 assaults per 1,000 population (n = 381). The neighbourhoods having the lowest number of assaults were Arcola East 0.7 per 1,000 population (n = 13), and

Normanview West with a rate of 1.6 per 1,000 population (n = 6).

4.5.1.1 Spatial Neighbours

Prior to conducting spatial autocorrelation, a preliminary test for polygon data clustering was done. This simple indicator determined whether the data were highly clustered or reflected only a low level of clustering; this, in turn, determined whether spatial autorcorrelative testing was needed. The Getis-Ord

General G high/low clustering test was conducted using the ArcGIS spatial analyst.

The results displayed in Figure 27 below indicated a cluster of high values that was not likely to be due to random chance (General G = 31.54, Z-score = 3.8

SD, p < 0.01).

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Figure 27 Getis-Ord General G High/Low Clustering Test Assault

4.5.1.2 Spatial Autocorrelation

The test for Spatial Autocorrelation of the data was the final statistical

calculation applied to the assault data; It determined whether the x and y locations, aggregated to a polygon level, were independent of each other (i.e., attributable to randomness) or instead, exhibited spatial dependence (Rogerson,

2001).

In this study, the observations were aggregated to a neighbourhood census boundary in Regina for 2005. The Moran’s I represented the observations in each neighbourhood and accounted for the spatial proximity of assault cases

between each neighbourhood boundary, as displayed in Figure 28.

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Figure 28 Spatial Autocorrelation of Assault

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Interpreting the spatial autocorrelation of the total assault incidents (n =

2,197) was first done through visual inspection. Upon examination, it was visually apparent that areas with little clustering (i.e., low crime areas, indicated in this figure by the colour blue) were close to each other, and that high crime areas

(i.e., the areas coloured red and orange) were also near one another.

The second form of interpretation was the analysis of the overall spatial autocorrelation for all neighbourhoods in Regina, represented by the Moran’s I

Index box located in the right-hand corner of the map. The Moran’s I results of all assaults in Regina in 2005 indicated a very high level of clustering (Moran’s I

Index = 0.03, Z-Score = 2.6 SD, p < 0.01). The diagram within the box demonstrates, on a scale of 1 (dispersed) to 5 (clustered), that the polygon neighbourhood data was clearly clustered, indicating a positive, highly significant autocorrelation within the data. After concluding that autocorrelation was present in the entire database, it was important to test each group (i.e., total 100%, model

70%, and test 30%) separately to see if the data was spatially dependent in each group of assault cases (see Figure 29).

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Figure 29 Spatial Autocorrelation of Assault Full, Model and Test Groups

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Finally, the interpretation of each dataset in Figure 29 displayed a high level of spatial autocorrelation for each distinct dataset. The Moran’s I results of the total assaults again indicated a very high level of clustering (Moran’s I Index =

0.03, Z-Score = 2.6 SD, p < 0.01), and the assault model group also

demonstrated a high level of clustering (Moran’s I Index = 0.04, Z-Score = 2.9

SD, p < 0.01). However, the assault test group also showed the same significant

clustering (Moran’s I Index = 0.04, Z-Score = 2.9 SD, p < 0.01).The diagram

within the box demonstrates, on a scale of 1 (dispersed) to 5 (clustered), that the

polygon neighbourhood data for all three databases showed a high level of

clustering, indicating a positive, highly significant autocorrelation within all three

datasets.

4.5.2 Break-and-Enter Data Polygon Results

After conducting polygon analysis on the assault data, the same

techniques were applied to the break-and-enter data. The aggregated break-and-

enter data were then cartographically displayed in Table 12 (n = 1,875) by each

neighbourhood in Regina 2005.

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Table 12 Break-and-Enter Counts, by Neighbourhood Break-and-Enter Rates /1000 in Regina 2005, by Neighbourhood Neighbourhood # of B & E’s Neighbourhood # of B & E’s

Arcola East 2.8 Dieppe 4.3

Prairie View 2.2 Glencairn *na

Twin Lakes 2.9 Glenelm *na Walsh Acres- Lakeridge 2.1 Core Group *na

Coronation Park 7.0 Al Ritchie 10.1 Argyle Park- Englewood 4.7 Lakeview 4.5

TBD5 *na Albert Park 1.9

Uplands 1.9 TBD2 *na

Northeast 9.3 Hillsdale 4.1

North Central 38.5 Gladmer Park 3.6

Regent Park 8.6 Boothill 4.1

Normanview 8.4 Normanview West 3.5 Rosemont-Mount Royal 12.9 Eastview 27.8

TBD1 0.0 Transitional Area *na

Downtown 845.5 Sherwood-McCarthy 3.6

Cathedral Area 12.6 Whitmore Park 2.0

McNab 10.9 Total n = 1,875 *Note: Some neighbourhood populations were unavailable due to industrial, transitioning and new emerging neighbourhoods prior to census collection. The total crime count includes neighbourhoods where populations were unavailable.

Initial assessment of the neighbourhood data in Table 12 indicated that the highest concentrations of break-and-enters by neighbourhood were located in the neighbourhoods of Downtown with a rate of 845.5 per 1,000 population (n = 520)

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and North Central rate of 38.5 per 1,000 population (n = 358). The North Central neighbourhood borders on the downtown area’s north side.

4.5.2.1 Spatial Neighbours

As discussed earlier, prior to conducting spatial autocorrelation, a preliminary test for clustering of polygon data (Getis-Ord General G high/low clustering test) was conducted using the ArcGIS spatial analyst. The results displayed in Figure 30 indicate that a significant high clustering of high values occurred (General G = 0, Z-score = 3.8 SD, p < 0.01).

Figure 30 Getis-Ord General G High/Low Clustering Test for Break-and-Enter

4.5.2.2 Spatial Autocorrelation

The final statistics computed on break-and-enter data utilized spatial autocorrelative techniques which, as discussed, determine whether the x and y

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locations, aggregated to a polygon level, were random (i.e., independent of each other) or whether they exhibited spatial dependence (Rogerson, 2001).

The break-and-enter point data observations were aggregated to a neighbourhood census boundary level in Regina for 2005 for this analysis. The

Moran’s I technique was used to determine the presence of autocorrelation

(further explained in Chapter 5). The Moran’s I results represented the break- and-enter observations in each neighbourhood and accounted for the spatial proximity of cases between each neighbourhood boundary (illustrated in Figure

31).

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Figure 31 Spatial Autocorrelation for Break-and-Enter

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Interpretation of the spatial autocorrelation evident in Figure 31 was of the total break-and-enter incidents dataset (n = 2,197). Visual inspection indicated that some low cluster areas (i.e., low crime areas indicated by the colour blue) were also clustered near each other, and that high crime areas (i.e., red and orange coloured areas) were clustered together, too. However, this clustering was not as visually apparent as it was in the assault analysis. Therefore, it would be expected that the autocorrelation existed, but that the statistics may have produced a slightly less obvious sign of high/low clustering than did the assault data.

Analysis of the spatial autocorrelation for all neighbourhoods was then conducted in Regina and was represented by the Moran’s I Index box located in the right-hand corner of the map in Figure 32. The Moran’s I results of all break- and-enters in Regina 2005 indicated a high level of clustering (Moran’s I Index =

0.01, Z-Score = 2.2 SD, p < 0.05). The diagram within the box demonstrated, on a scale of 1 (dispersed) to 5 (clustered), that the polygon neighbourhood data were clearly clustered (4 out of 5), indicating a positive, significant autocorrelation within the data. Note, however, that the assault data were rated a 5 out of 5 and showed an even higher level of significance with respect to the clustered relationship.

Knowing that autocorrelation was present in the entire break-and-enter database, it was important to test each group (i.e., total 100%, model 70%, and test 30%) separately to see if the data were spatially dependent in each group, as illustrated in Figure 32.

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Figure 32 Spatial Autocorrelation for Break-and-Enter Full, Model and Test Groups

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Similar to the assault interpretation, the analysis of each dataset in Figure 32

displayed a higher than expected level of spatial autocorrelation for each distinct

dataset. As noted previously, the Moran’s I results of the total break-and-enters

indicated a significant level of clustering (Moran’s I Index = 0.01, Z-Score = 2.2

SD, p < 0.05). The break-and-enter model group also illustrated a significant level

of clustering (Moran’s I Index = 0.01, Z-Score = 2.2 SD, p < 0.05), and the

assault test group showed the same significant clustering (Moran’s I Index =

0.01, Z-Score = 2.0 SD, p < 0.05).The diagram within the box demonstrated, on a

scale of 1 (dispersed) to 5 (clustered), that the polygon neighbourhood data for

all three databases showed a moderately high level of clustering, thus indicating

a positive, significant autocorrelation within all three datasets.

4.6 Assault and Break-and-Enter Comparative Results

4.6.1.1 Standard Deviational Ellipses and Mean Centre Analysis

A persistent pattern emerged as the analysis of all the neighbourhood

data was conducted. It indicated that both static crime (assault) and dynamic

crime (break-and-enter) demonstrated clustering throughout the Downtown and

the North Central communities. Two more tests were then done to examine the

relationship between assault and break-and-enter.

First, a standard deviational ellipse and mean centre examination was

done to determine the shapes, dispersion, and average x and y coordinate

location information. As discussed in previous sections, the mean centre was a

simple descriptor of the distribution representing only the mean of the x and y

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coordinates (Levine, 2004), while the standard deviational ellipses provided a

single statistic illustrating their dispersion in two dimensions on a map (Levine,

2004). The ellipse and the mean centre provided a visual and statistical depiction

of the dispersion of the data prior to conducting Kriging interpolation tests which

would comprise the final test of the interaction of these two datasets.

Table 13 compared the mean centre for the x and y coordinates of the total break-and-enter dataset to that of the total assault dataset. Statistically, the mean centre and the standard x and y deviations from the mean appeared to be

statistically similar to one another. This seemed to indicate there was not a large

discrepancy between the means of both datatsets, but that there was a minor

difference.

Table 13 Mean Centre for Assault and Break-and-Enter

Mean Centre Break-and-Enter and Assault Results

Standard Standard Dataset Mean X Mean Y Deviation Deviation X Y

B-&-E Total 100% -104.617793 50.454208 0.027443 0.016020

Assault Total 100% -104.614090 50.455811 0.026441 0.015349

However, it was also important to compare the dispersion of the x and y coordinates, rather than only the mean. Statistically, the length and area of the standard deviational ellipses illustrated in Table 14 showed slight differences.

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Table 14 Length and Area of Standard Deviational Ellipses, Assault and Break-and-Enter

Length and Area of Standard Deviational Ellipses

X Axis Area of Dataset Y Axis Length Length Ellipse

B-&-E Total 100% 2.384 mi 3.971 mi 7.433 sq mi

Assault Total 100% 2.534 mi 3.659 mi 7.281 sq mi

As a result of the slight variations in the length and area of the standard deviational ellipses, it was crucial to cartographically display the ellipses for visual interpretation, as well.

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Figure 33 Standard Deviational Ellipses for Assault and Break-and-Enter

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As depicted in Figure 33, the standard deviational ellipses for both break- and-enter and assault showed similarities, but they were not an exact match. For example, both ellipses indicated that most of the crime was happening at the centre of Regina in the downtown area, but that the dispersion was slightly different. This may seem more uncommon for break-and-enter; however, two neighbourhoods in the downtown core (the two major clusters) contained a high number of residential break-and-enters, which in turn created a tighter ellipse with the mean centre located in the city center.

The standard deviational ellipse for break-and-enter was slightly longer, indicating a wider spread of that crime throughout the city as compared to assault. This made intuitive sense, as you would expect to see a larger dispersion of break-and-enters owing to the nature of where the crimes must occur (in static neighbourhoods). The break-and-enter ellipse also extended slightly further southwest of the assault ellipse, which may be due to the concentration of housing further away from the downtown core, whereas the assault ellipse indicated slightly less dispersion and a tighter dispersion slightly northeast of the break-and-enter ellipse. Finally, visual analysis of the mean centres also indicated that the average break-and-enter was occurring close to, but slightly more southwest of, the assault incidents.

4.6.1.2 Kriging

The results of the Kriging tests for the assault and the break-and-enter model and test groups confirmed the original hypothesis that Kriging was a functional tool able to create prediction surfaces of criminal events. The

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assumption proposed at the outset of this research was that static crime, such as break-and-enter, would produce a stronger predictive model than would a dynamic crime such as assault; however, the results did not support this assumption.

For example, the results of the assault data for the smoothed Georisk surface displayed the correlations to have a risk mean of 0.127 with a standard deviation of 0.218. The correlation coefficient was 0.613 with a Z-Score of 2.233, thus indicating a strong and highly correlated surface model, whereas the break- and-enter model had a risk mean of 0.146 with a standard deviation of 0.233.

The correlation coefficient was 0.551 with a Z-Score of 1.74, indicating that the model had only a moderately significant correlation, as seen in Figure 34.

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Figure 34 Assault and Break-and-Enter Kriging Correlation

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Upon initial assessment of the difference between the break-and-enter model group and the assault model group, it was evident that the data displayed a stronger correlation of the predictive surfaces for assault than they did for the break-and-enter group. This correlative finding challenged one of the principal

assumptions of this study, a topic that is discussed in more detail in the following chapter. However, based on these surprising results and the fact that the majority of the results demonstrated that the patterning of the break-and-enter and

assault hot spots were very similar, a final Kriging surface was created to test the

correlation between the assault model group and the prediction of the break-and-

enter Kriging surface.

Not surprisingly, it was found that the predictive Georisk surfaces for

assault were correlated to the break-and-enter model, producing just a slightly

higher correlation than that of the model and test groups for break-and-enter

alone. It was found that the correlation produced a risk mean of 0.16 with a

standard deviation of 0.25. The correlation coefficient was 0.612 with a Z-Score

of 1.812, indicating a correlation between the assault and the break-and-enter

risk surfaces.

The next chapter continues discussing the impact and implications of this

study on current and future research based on temporal and spatial findings. It

also describes the benefits and implications these models may have on public

safety policy.

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5: DISCUSSION

This thesis focused on three main objectives as it created robust crime prediction models for static and dynamic crime. The first was to create and test a geostatistical model of two crime types, static (break-and-enter) and dynamic

(assault), to determine whether geostatistical techniques such as Kriging might create valid predictive models using crime data.

The second objective was based on the model’s successful creation of valid risk surfaces of static and dynamic crime, thus a correlational test would determine which model would more accurately assess risk (i.e., have higher predictive validity). It was proposed that the static model of break-and-enter would create a more reliable risk surface as compared to the dynamic crime of assault, owing to the issue of mobility.

The final objective was to develop new geostatistical software (Crime Risk

Assessment Software) to determine the feasibility of implementing simpler risk software to replace the currently available but far more complex systems that create robust predictive models .

The study’s three objectives were met, and results generate several implications for future risk analysis. This chapter offers a detailed discussion of these implications and other findings concerning the Geography of Crime.

Specifically, the comprehensive models created from this study’s results are reviewed in the context of the study area’s dynamics, and considerations for

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future research and policy implications based on the results are examined as

well.

5.1 Findings

The results clearly supported the study’s main objective – the Kriging

technique successfully modelled both static and dynamic crime. It was, however,

proposed that it would more effectively model static, rather than dynamic, crime.

owing to the mobility factor, yet the results demonstrated otherwise. A

comprehensive examination of assault illustrates several key discussion points

relevant to the overall impact these findings have on the Geography of Crime.

The following section presents the impact of the results specific to the field of

criminology.

5.1.1 Temporal Findings

With respect to temporal analysis, it was found that most assaults

occurred between 9:00 and 10:00 pm (n = 129, 5.8%) and between 6:00 and

7:00 pm (n = 119, 5.4%). However, an interesting temporal pattern indicated that

the clustering of assault times occurred between 2:00 and 7:00 pm (n = 573,

26%) and again from 9:00 pm to 4:00 am (n = 744, 33.9%).

According to Ratcliffe (2002), temporal patterns tend to reflect the routine

activities of the victims rather than of the offenders. Brantingham and

Brantingham (1995a) described how we might expect a tendency for certain

crimes such as assault to also cluster owing to crime generators and attractors.

Brantingham and Brantingham (1995a) note that crime generators are areas to

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which large numbers of individuals are attracted, potentially for various unrelated reasons, but that once they arrive, they may end up committing a crime

(Brantingham & Brantingham, 1995a). For example, crime is more likely to result wherever there may be both a large concentration of targets and a better than average opportunity to commit a crime. A drinking establishment offers a prime example of such an intersection of time and place.

The example used in Chapter 2 illustrated how people typically go to a drinking establishment to have fun and drink. They do not generally set out with the intention of committing an assault. However, the concentration of people along with drinking and/or drugs may encourage poor decision-making behaviour, thereby generating criminal behaviour. Crime may thus be facilitated by a combination of all the external environmental factors surrounding the

‘location’, rather than being created solely by an offender targeting a bar to commit a crime.

In addition to the concept of “bar as crime generator”, the area surrounding it may also be considered a crime attractor. For example, crime generators are specific “places, areas, neighbourhoods, or districts which create well-known criminal opportunities to which strongly motivated, intending criminal offenders are attracted because of the known opportunities for particular types of crime” (Brantingham & Brantingham, 1995a, 8). An example of a crime attractor is a typical city’s prostitution stroll – a location often well known for its illegal sex and drug traffic. Criminals are attracted to this area in order to commit criminal offences associated with drugs or prostitution. Thus, though a bar may be most

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often viewed as a crime generator, it could also be situated in a high crime area considered by many to be a specific place where people go to sell or buy drugs.

Therefore, the drinking establishment may not only generate crime, but the surrounding area could attract offenders planning criminal activity.

The study’s assault results clearly indicated that a large number of assaults (n = 1,317, 60%) occurred between 2:00 and 7:00 pm and from 9:00 pm to 4:00 am. Additionally, the majority of the assaults occurred downtown amidst a lower income area with numerous drinking establishment locations. As Nelson,

Bromley, and Thomas (2001) pointed out, large portions of non-domestic, violent personal crimes typically occur in the city centre . Shepherd and Brickley (1996) also researched the link between alcohol and violent crime. This was indicative of a crime generator in that the use of alcohol and/or drugs may contribute to assaultive behaviour, while the bar being located in the highest crime area in

Regina was also indicative of a crime attractor. Figure 35 demonstrates that

Statistics Canada found the highest concentration of violent crime in Regina in exactly those areas identified by the Kriging risk model – downtown and the surrounding areas.

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Figure 35 Kernel Density Distribution of Violent Incidents, Regina, 2001 (Wallace et al., 2006, 12)

The downtown and its immediate surroundings can therefore be considered a

crime attractor, while the drinking establishments located at or near the assault

locations could be perceived as crime generators within that high crime area.

As expected, the temporal dynamics of break-and-enters were a direct

contrast. Their pattern demonstrated a concentration occurring between 9:00 am

and midnight (n = 1,658), with the highest concentration occurring from 4:00 to

5:00 pm (n = 154). Not surprisingly, the lowest occurrence of break-and-enters occurred between 5:00 and 6:00 am (n = 15). However, related research

indicates that peak times vary widely. For example, Rachel Boba described how,

in a 2009 study, peak break-and-enters occurred Monday through Friday from

10:00 pm to 4:00 am. Yet another study conducted by Cohen and Rotton (2000)

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demonstrated that the most frequent break-and-enters occurred Monday through

Thursday between 3:00 and 9:00 pm, whereas Friday to Sunday showed a higher frequency of burglaries between 9:00 pm and 3:00 am

In general, as Ratcliffe pointed out (2005), researchers seek to understand the changes and temporal patterns in spatial distributions for many different reasons, including understanding the early detection of crime, diffusion or displacement, or the changing risk and opportunity structures caused by socioeconomic development (Ratcliffe, 2005). However, as Ratcliffe points out, many of the traditional measures used to determine spatial temporal changes are limited (2005). Unfortunately, as that particular study did not focus on the relevant times involved, more research must be done to separate the time of day from the day of the week and the season in order to fully understand this issue and to effectively compare it in more detail with the research currently available.

5.1.2 Comprehensive Model Overviews

As a complete geostatistical Kriging risk model, Figure 36 displayed the results of the assault model and highlighted some interesting findings with respect to the Geography of Crime while also presenting some of the model’s weaknesses.

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Figure 36 Comprehensive Model of Assault

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The model demonstrated the existence of spatial clustering using both the and the tests in Figure 36. However, as a footnote in Chapter 4 points out, a problem associated with conducting the CSR tests was the statistical assumption of continuous surface (Unwin & Hepple, 1974). This statistical assumption was violated in this case because crime occurs on street networks rather than on a continuous surface; it was thus important to add several other analytic components to verify the results. For example, the nearest neighbour analysis commonly used in the criminology field carries the same statistical assumption of a continuous surface. Therefore, by referencing the total assault incidents dataset, the mean nearest neighbour (Nna)28 distance was 0.043 miles, whereas the mean nearest neighbour ‘random’ distance expected was 0.094 miles. The nearest neighbour index was therefore 0.453 with a Z-value of -41.308. These results were highly significant (p<0.01), indicating that the nearest neighbour distances of assaults in Regina were less than would be expected were the results random.

Once again, this confirmed that these results were not random and not due to chance variation. However, we still had to be cautious regarding this violation of the continuous surface assumption. Therefore, as Chen et al. (2004) recommended (see the discussion in Chpt. 2), a multi-statistical method was employed in order to provide a comprehensive and more robust model of analysis in this particular case.

28 The nearest neighbour analysis was conducted with the defined neighbours of 50, no border correction, and a surface area of 114 kms.

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As Figure 36 illustrated, spatial intensity, standard deviational ellipses, and mean centres were utilized to confirm dispersion and to portray the spatial intensity surface contour plots of the total assaults in Regina. Consistent with the expectations from the CSR and spatial neighbours results, the contour plot illustrated very tight point pattern intensity with contours very close together. The surface plot illustrated only one large intensity of assault clusters, thus reflecting an extremely high concentration of assaults at the city centre with a slight dispersion throughout the rest of the city.

In relation to the Geography of Crime, this was somewhat typical patterning consistent with Crime Pattern Theory, but it did not entirely fit the theory. For example, in terms of assault, according to the limited research available, one would expect to see higher concentrations surrounding the downtown area with its crime generators such as drinking establishments, clubs, etc. As was pointed out in the previous chapter, the Kriging map illustrated a definite concentration of assaults around drinking establishments. We do not, however, see a very wide spread throughout the rest of the city.

This lack of spread of occurrences might be caused by a limitation in this study concerning the size of the study area. For example, the City of Regina has a population of only 194,971 CMA in 2006 (Wallace et al., 2006). In relation to the size of other major Canadian cities, it ranks only 18 out of 25 (Wallace et al.,

2006). Drinking establishments and other similar facilities tend to cluster in the downtown section of small cities with limited populations like Regina. Therefore,

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the lack of other concentrations in this study may in fact be limited or constrained

by the city’s geography and/or size.

Despite this limitation, the predictive software should still theoretically be

accurate in terms of its predictive capability. Therefore, after calculating the initial

risk surface through the crime risk software, Georisk smoothed surface output

displayed the areas which were statistically deemed high risk for repeat assaults.

The calculation for the correlations between the assault model and test group

demonstrated the risk mean of 0.127 with a standard deviation of 0.218. The

correlation coefficient was 0.613 with a Z-value of 2.233, indicating that the model and the test group were highly correlated and confirming the accuracy of the measure used.

In analyzing the difference between the assault model group and the test

group, the objective of this study was deemed correct in that it did accurately

portray where one would expect a predictive surface to illustrate a high-risk area

based on all the other tests calculated prior to Kriging.

Nevertheless, the assumption of this study was that the Kriging would not

work as well for dynamic crimes such as assault owing to that crime’s mobility

factor. Therefore, a correlative test was conducted using the Kriging technique on

a static crime, in this case break-and-enter, to determine whether the assumption

was correct.

As Figure 37 indicated, break-and-enters were concentrated in only one

particular area, but clusters were more dispersed throughout the city. According

to the break-and-enter literature, we would expect to see different patterns for

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these crimes as they occur in very different locations. For example, residential break-and-enters need a static point (e.g., a house) in order for the occurrence to take place, whereas assault is mobile and is considered a dynamic crime with the potential to occur anywhere. By examining the contour plots, it was apparent that assaults were slightly less dispersed than were break-and-enters.

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Figure 37 Comprehensive Model of Break & Enter

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Figure 37 displayed varying high risk areas throughout the city, yet the Kriging technique used on the break-and-enter locations still indicated that a high level of crime similar to that of assault was occurring in communities neighbouring the downtown core. The mean nearest neighbour distance for break-and-enter was

0.040 miles, whereas the mean nearest neighbour ‘random’ distance expected was 0.09 miles. The nearest neighbour index was therefore 0.452 with a Z-value of -43.417. When compared with assault using the total assault incidents dataset, the mean nearest neighbour distance was 0.043 miles, while the mean nearest neighbour random distance expected was 0.094 miles. The nearest neighbour index was therefore 0.453 with a Z-value of -41.308. Both of the results were highly significant (p < .01). However, despite the presence of more clusters that are further dispersed in the case of break-and-enters, the actual occurrences of assault demonstrate only slightly tighter occurrences happening closer together.

Comparable to the results of the assault data, the Georisk smoothed surface displayed areas which were statistically deemed a high risk for a repeat break-and-enter to occur. The correlation between the break-and-enter model and test group produced a risk mean of 0.146 with a standard deviation of 0.233.

The correlation coefficient was 0.551 with a Z-Score of 1.74, indicating that the model and test group were significantly correlated (see Figure 37).

As was noted, the original hypothesis of this study purported that Kriging, if successful, would better predict static crime (such as break-and-enter) than it would dynamic crime (such as assault). Interestingly, this was not the case. The

Kriging technique demonstrated the opposite. The assault model (dynamic)

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produced higher accuracy and significance levels than did the break-and-enter model. However, it is important to note that even though the crime of assault was considered a static crime, as seen in the literature review, such crime tends to cluster around static locations such as drinking establishments. This element of stationarity was an important consideration in the unanticipated result. Whether this may have been a product of static crime event locations, city size, and/or geographic layout is discussed further in the limitations section.

Finally, it was important to test the significance, if any, of both crimes together. As the results indicated, the predictive correlation produced a risk mean of 0.1599 with a standard deviation of 0.2496. The correlation coefficient was

0.6121 with a Z-Score of 1.8122, indicating a correlation between the assault and break-and-enter risk surfaces. Once again, the city’s limitations may explain why both crimes occurred in similar areas, and further research to test the same algorithms on a larger, more defined city will determine whether this conclusion is in fact correct.

5.1.2.1 Regina Crime Context

When using any innovative technique in criminology to analyze crime, it is imperative to put the analysis into the context of other criminal, housing, and population issues in the city being studied. Upon reviewing the assault results, a study done by Statistics Canada provided an overview of violent crime with respect to Regina’s land-use and housing. For example, Figure 38 highlighted the incidence of high and low crime based on the characteristics of particular neighbourhoods.

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Figure 38 Reproduced Chart: “Land-use and Housing Characteristics for Violent Crime” (Wallace et al., 2006, 17) Land-use and housing characteristics in neighbourhoods with high and lower rates of violent crime, Regina, 2001

80 70 Lower-crime 60 High-crime 50 40

Mean % Mean 30 20 10 0

According to Figure 38, more violent crime occurred in areas with the following characteristics: higher density, a greater percentage of dwellings in need of major repair, areas that were older (pre-1961), and those with more unaffordable housing (Wallace et al., 2006). Figures 39 and 40 also demonstrated that increased rates of violent crime tended to occur more often in areas exhibiting high mobility, a high concentration of Aboriginals, more female-headed lone parent families, and finally, in areas populated by persons sharing lower income, employment, and education levels.

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Figure 39 Population Characteristics for Violent Crime (Wallace et al., 2006, 18) Population characteristics in neighbourhoods with high and lower rates of violent crime, Regina, 2001

30 25 20 15

Mean % Mean 10 5 Lower-crime 0 High-crime % Residential % Aboriginal % Female Lone- Mobility (1 yr Parent Families Movers) Source: Statistics Canda, Canadian Centre for Justice Statistics, Incident-based Uniform Crime Reporting Survey, 2001

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Figure 40 Socio-economic Characteristics for Violent Crime (Wallace et al., 2006, 19) Socio-economic characteristics in neighbourhoods with high and lower rates of violent crime, Regina, 2001

60 50 40 30

Mean % Mean 20 10 0 Lower-crime High-crime

1. Median household income in $1,000s. Source: Statistics Canada, Canadian Centre for Justice Statistics, Incident- based Uniform Crime Reporting Survey, 2001

Police categorize assault as a violent crime. Interestingly, the areas within

Regina where the greatest concentration of assaults occurs is in the downtown communities (Wallace et al., 2006). Not surprisingly, this study’s Kriging results similarly indicated a high level of assault concentration there.

In terms of the high concentration of Aboriginals in the populations of neighbourhoods prone to high levels of violent crime, Regina has historically been known for its over-representation of Aboriginal offenders in the city’s justice system. The Statistics Canada report on Regina compiled in 2006 by Wallace et al. noted that, when modelling the proportion of Aboriginal people in a

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neighbourhood with crime rates, 53% of the variation in violent crime is explained by the variable of Aboriginal population alone.

Property crime results demonstrated a similar dynamic at work; the

Aboriginal population variable explained 34% of the variation in the rate of

property crime. Figure 41 illustrates the specific breakdown for Regina.

Figure 41 Population Characteristics for Property Crime (Wallace et al., 2006, 19) Population characteristics in neigbourhoods with high and lower rates of property crime, Regina, 2001

25 20 15 10 Mean % Mean 5 Lower-crime 0 High-crime % Residential % Aboriginal % Female Lon- Mobility Parent Families Source: Statistics Canada, Canadian Centre for Justice Statistics, Incident-based Uniform Crime Reporting Survey, 2001.

This study’s purpose was of providing a methodological review, and not

explanatory, thus the reasons why areas with higher concentrations of Aboriginal

populations were found to produce higher levels of crime could be the focus of

future research. However, as noted earlier, the context of where the crime was

occurring geographically was just as important as the social context within these

communities. The objective of this study was the techniques used to predict the

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location of criminal activity, but understanding where and why constitute fruitful future research questions.

Just as with violent crime (see Fig. 38), property crime most often occurred where there were higher percentages of multiple family zoning, a higher percentage of dwellings in need of major repair, areas considered to be older

(pre-1961), and areas with higher levels of unaffordable housing (Wallace et al.,

2006).

Figure 42 Land-use and Housing Characteristics for Property Crime (Wallace et al., 2006, 18) Land-use and housing characteristics in neighbourhoods with high and lower rates of property crime, Regina, 2001

80 70 60 50 40

Mean % Mean 30 20 10 0 Lower-crime High-crime

Source: Statitics Canada, Canadian Centre for Justice Statistics, Incident-based Uniform Crime Reporting Survey, 2001

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Similar to violent crime, less property crimes were committed in areas

populated by persons sharing lower education and income levels and less regular employment (Wallace et al., 2006).

Figure 43 Socio-economic Characteristics of Property Crime (Wallace et al., 2006, 20) Socio-economic characteristics in neighbourhoods with high and lower rates of property crime, Regina, 2001

Mean % Mean Lower-crime 20 High-crime 10

0 % Receiving % Holding a % Below Low- % Median Governement Bachelors income Cut- Unemployed Household Transfers Degree off Income1 1. Median household income in $1,000s Source: Statistics Canada, Canadian Centre for Justice Statistics, Incident-based Uniform Crime REporting Survey, 2001.

This study’s results, in particular, have an impact not only upon theoretical

matters, but it also significantly affects policy and policy decision making.

5.2 Public Safety Implications

The pressing question is, how do risk models like the one created in this

study enhance public safety policy? The use of risk analysis in public safety

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policy is rather complex because action is not precipitated simply because a risk

is evident. Governments are responsible to weigh all relevant information in order

to analyze a given situation and decide whether it calls for further investigation or

for action. As Tim McDaniels (2002) notes, governments have an extremely

broad and complex responsibility as far as “setting regulatory frameworks and

policy directions for managing and balancing complex threats to our collective

environmental, social, and economic well-being” (p. 1). Although experts play a

vital role in describing and assessing risk, the ultimate decision lies with elected

officials (McDaniels, 2002). With such difficulties surrounding the assessment of

risk, positive and negative outcomes are expected. Therefore, the following

section illustrates the use and misuse of risk and hazard models with respect to

public safety policy and with specific respect to this study.

5.2.1 Risk and Hazard Model Uses

The process of policy development and policy analysis are extremely

detailed and complex. The purpose of this section is not to explain these

approaches, but rather, to shed light upon the application of various models in

policy development and analysis.

In order to propose, develop, or change a policy, a significant problem must first be identified. The fact that risks or hazards may be identified as a concern or a problem does not necessarily facilitate action (Tobin & Montz,

1997). As policymakers deal with numerous issues each day, risks and hazards

comprise only one subset of problems (Tobin & Montz, 1997). Once problems

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are identified, policymakers then prioritize them based upon their severity before

responding. However, Tobin and Montz (1997) point out that the main goal of

hazards policy is to reduce exposure and vulnerability. The question then

becomes an issue of how policymakers use risk and hazard models to create,

change, or improve public safety policy.

As was outlined in Chapter 2, several models have been used to evaluate hazardous situations. In order to conduct analyses using these models, appropriate data must be available. In the past, it has been difficult to spatially depict risks and hazards. More recently however, advances in data availability and in analytic methods (this study offers one such example) have improved investigations leading to advancements in the reporting of hazards or risks.

Specifically, Elliot and Wartenberg (2004) mention that a major advancement has developed in the reporting of disease risks (spatial epidemiology) at a national and/or regional level. Improvements in data quality and availability increase and improve the evidence required to persuade policymakers to take action.

Spatial epidemiology is only one form of risk surface used in public safety policy. Table 15 lists current areas of Canadian government intervention.

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Table 15 A Sample of Risks Subject to Government Intervention (Hill & Dinsdale, 2001, 46) Transportation Economic or Financial . Automobiles, motorcycles (a) Related to financial instruments and . Trucks institutions . Railroads . Securities (debt and equity) . Ships, barges, other watercraft . Banking and other financial institutions . Pipelines (oil, gas, water, commodities) . Insurance companies . Electricity (especially electromagnetic fields) . Pension plans Environment . Deposit insurance . Climate change (b Related to the purchase of products . Air, water, land pollution (e.g., acid rain, urban . Product labelling, including smog, contaminated sites) trademarks . Forestry practices . Weights and measures . Toxic substances . Misleading advertising or marketing . Biodiversity and endangered species practices . Fisheries . Quality assurance (e.g., birth control . Ozone depletion devices) Natural Resources . Efficacy of professional services . Access and use of renewable resources (fish, (c) Related to income level and flow timber, water, wildlife) . Employment insurance . Access and use of non-renewable resources . Canada pension plan/welfare (petroleum, coal, natural gas, minerals) payments . Worker s compensation . Crop insurance . Disaster relief (ad hoc) Consumer Products Human Safety . Automobiles (e.g., seatbelts, airbags, bumpers, (a) Infrastructure running lights, fuel standards) . Dams, bridges, utility lines, roadways, . Drugs (for humans and animals) pipelines . Medical devices (b) Natural disasters . Children’s toys, clothes, cribs, car seats, etc. . Weather events (hurricane, tornado, . Explosives flood, ice storm, blizzard, drought, . Pleasure boats (e.g., Jet Skis) avalanche) . Tires . Earthquakes . Forest or grassland fires Food Security . Food contamination during production and (a) National security distribution . Defence against invasion or attack . Food labelling . Protection against subversion from . Pesticide application and residuals in food within . Bovine growth hormone in milk (b) Personal security of citizens . Irradiation . Police . Genetically modified foods . Fire fighters Technology Rights . Nuclear power . Human rights (including the Charter) . Biotechnology . Collective bargaining . Genetic engineering . Humane treatment of animals . Information technologies Occupational . Workplace safety

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As table 15 illustrates, numerous risks are subject to government intervention.

Studies such as this have a role to play with respect to developing security policies as seen above. As previously mentioned, risk and hazard models are techniques that help create, change, or analyze public safety policy. Juliana

Maantay notes that spatial information actually enhances policy formulation and facilitates the decision-making process (2002).

This is no different from the current study. New software such as the

Crime Risk Assessment Software described in this study develops new ways to visualize and statistically analyze the risk of crime. However, limitations or misuses of software and data can occur, and it is therefore important to discuss it in terms of policymakers’ assessment of risk.

5.2.2 Risk and Hazard Model Misuses

Where there are uses of risk and hazard models, there tend also to be misuses, though we might more accurately substitute the term “ill-informed choices” for misuse, as such instances are rarely intentional; for example, the most common misuse of risk surfaces or hazard models is the inappropriate use of evidence or research.

Inappropriate use can occur when policy is formed based on research that has not been conducted thoroughly. An example that was touched on earlier in this paper concerns the modifiable areal unit boundary problem (MAUB). The

MAUB becomes a problem when the data are aggregated. Unfortunately, census data in Canada is not yet easily accessible or available at a level that can be represented by each individual residential location or block, thus census data

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were aggregated up to an arbitrary boundary created either by government (e.g.,

census tracts or enumeration areas), by police districts, or by health districts, to

offer but a few examples.

The census data are aggregated specifically to the census divisions, thus

providing one number uniformly across an entire boundary. For example, five

neighbourhood blocks may be combined to equal one census tract. The average

income for that census tract may be $40,000. Because we do not know the

income for each house, or even for each street, the boundary shows $40,000

uniformly across that entire census tract. This becomes a problem when incident

data are typically presented in point form (to a specific geographic location by x/y

coordinates). In order to overlay the census and incident data, both forms should

be at the same level for analysis. When this happens, the incident data must be

aggregated up to a larger unit (the census tract) in order to have spatially

matched data. The problem is that once the incident data are aggregated to a

larger unit like a census tract, the spatial software depicts the incidents uniformly

across the boundary, regardless of their location within that census tract.

Data aggregated to the level of governmental units such as cities or countries is less reliable than data aggregated to smaller units (Maantay, 2002).

Unfortunately, this problem can occur even with smaller units, and it could result

in substantial differences, depending on the unit chosen. Smaller units may

underestimate and larger units may overestimate, or visa- versa. Again, it may

not be accurate to refer to that as an actual misuse.

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Unfortunately, to date, there has been no direct solution to the MAUB problem. There have been some very creative attempts to solve it, and many researchers currently use them (see, for example, Chen et al., 2004; Poulsen &

Kennedy, 2004). These range from using street level data, to the dasymetric mapping discussed previously in this thesis, to multiple analysis at multiple levels of aggregation. Until data are at a smaller level for analysis, models involving a spatial component must still be viewed with caution when conveying results to policymakers and to the public. Policy decisions cannot be made solely on geographic analysis unless multiple levels of analysis have been conducted. If not, policymakers will be drawing conclusions based upon the unknown reliability of the results.

A second form of misuse is referred to as the “cry wolf” syndrome. As

Wesley Wark (2002) explains, there is a lurking danger over this syndrome where a cycle of warnings to the public (based on evidence from the risk models) is then followed by the non-appearance of predicted threats. Sadly, since the

9/11 terrorist attacks, Americans, fearing more terrorist attacks, have been on a much heightened alert level. Shortly after 9/11, the Homeland Security Advisory

System (U.S. Department of Homeland Security, 2005) warning system was created to alert citizens of potential threats. This system has five security levels ranging from low to severe.

In July 2005, terrorists left bombs on the London metro system in England.

The response from the United States was to elevate the American terrorist alert advisory system for the entire mass transit system across the country. They

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elevated the advisory to code orange, indicating that a high risk of attack was

possible (U.S. Department of Homeland Security, 2005).

As there was no intelligence indicating any potential American attack, the

Advisory System was raised as a precautionary measure owing to the London-

based incident. The problem with such a decision is that eventually, according to

the cry wolf syndrome, such a cycle of warnings may eventually lead to loss of

reputation and credibility on the part of the intelligence agencies and government

(Wark, 2002). Though balancing risk and communicating a viable threat is an extremely difficult process, sounder decisions may have to be made in similar

situations such that alerts are not issued when the available evidence does not

support it.

The final misuse discussed here is more a matter of ill-informed research

and inappropriate study context. It concerns the blind faith that researchers,

policymakers, and analysts place in software. As David Vose explains, many

have faith that the software they purchase will run risk models and perform

credible risk analysis (1997), but unfortunately, this is not always the case. As

this thesis illustrates, several levels comprise risk and hazard analysis. I have

only touched upon some of the statistics and calculations utilized. Building a solid

model is an extremely complex process that draws upon both quantitative and

qualitative methods. Researchers, policymakers, and analysts therefore need to

educate themselves with respect to the statistics behind risk and hazard

modelling prior to interpreting and communicating results from the analysis to

prevent errors from occurring in the models.

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5.2.3 Current Implications

First, when discussing the use and misuse of software, the objective of this study was to present a newer crime prediction tool using newly developed software, a process that raises several concerns. Initially, the cost of developing

and selling the software can be an issue. As Paulsen and Robinson (2004) point

out, it is not only costly to buy the software, but there is also a high cost

associated with training professionals how to use it. There is a great deal of

software that can produce many different forms of risk models, but one must ask,

at what cost, and with how much expertise?

Another issue is related to the accuracy of the risk and hazard models

created. As Boba points out, “the methods and analysis are only as good as the

data used” (2009, 289). For example, many tests used in the past have violated

statistical assumptions – this thesis highlighted a few examples. One must use

caution when reporting results where violations occur. Additionally, it is not only

the data that are important; the analyst computing the model must also be highly

trained to increase levels of accuracy and reliability. If the analyst is not

appropriately trained, mistakes can occur.

Analysis in this study was conducted using multiple techniques in order to

account for this issue. For example, instead of only employing Kriging techniques

to address the objective, other methods such as nearest neighbour, spatial

intensity plots, and spatial autocorrelative tests, to list some examples, were

used to confirm the results and create a more robust spatial predictive model.

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Another implication of this study concerns the lack of spatial research on

assault. As Nelson, Bromley, and Thomas point out, “research on the micro-

spatial geography and temporal characteristics of violent crime has been

neglected in favour of identifying broader patterns” (2001). Without micro-spatial

analysis of violent crimes such as assault, the only focus surrounds the broader

patterns across regions. Therefore, we tend to lack finely detailed analysis on

particular problem areas, businesses (i.e., alcohol establishments), and

neighbourhoods. In particular, assault research is extremely deficient in terms of

detailed spatial and temporal analysis. In order to create more robust Kriging models of prediction, more research is needed in these areas.

Finally, in this study, the data was limiting in the following ways: it was

several years old, it covered only a one-year period, and it was relatively small, owing to the city’s size. Therefore, prior to implementing any policy related to

Kriging techniques used to predict future crime, further confirmatory research absolutely must be done.

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6: CONCLUSION

“Human behaviour may not be totally predictable, but it’s usually

reasonably easy to predict.” Ontheroadto1m, 2009

This quote can be found on a critical blogging website that was cited as being

one of the top 10 worst quotes on Twitter.29 Specifically, this website (On the

Road to 1 Million) stated that “we don’t know for sure who wrote this sentence, but you can clearly detect the words of an economist. Before the banks stopped lending” (Ontheroadto1m, 2009).

This quote may have some merit, if not from an economist’s perspective,

then at least from an environmental criminologist’s viewpoint – human behaviour is never completely predictable. However, despite the fact that we probably will

never be able to predict behaviour to a 100% certainty, the reality is that most

behaviour, given enough known variables, can be foreseen relatively accurately.

Even though this belief is not commonly shared by all criminologists, there

is no denying the predictable nature of human behaviour. For example, most of

the time, most people take the same seat every time they have a meal at their

kitchen table. We generally take the same route to go to work. More often than

not, we take the same roads or paths whenever we go to school, or shop for

29 Twitter is a relatively new social networking and blogging website that allows messages to be sent and received across the Internet.

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groceries each week. If we can choose whether to walk uphill or down to get to

our destination, most of us take the easier, downhill route. Most of us park where

lighting is brighter rather than in the darkest corner of the lot, as the increased

visibility provides a greater feeling of security. Of course, there will always be

deviations from these common paths but, in the final analysis, a great deal of

behaviour is routine or predictable.

The main objective of this thesis was to conduct a methodological review,

specifically using reported assault and break-and-enter crimes in Regina in order to first explore spatial-temporal patterns of crime and to develop and use hazard- risk modelling to improve methods for predicting future crime concentrations.

Second, in order to explore and improve current hazard-risk methodological models in criminology, new software was created for this thesis (Crime Risk

Assessment Software). The software was used to create a geostatistical risk model of two crime types, assault and break-and-enter (dynamic and static, respectively), to determine whether geostatistics, specifically Kriging techniques, could create strong predictive risk surfaces of these crimes.

The benefit to meeting these objectives was not only to add to the growing body of spatial literature, but if successful, we should be able to create more robust and predictive crime analysis techniques to analyze both static and dynamic crime. Having successfully implemented the Kriging technique for this purpose, an attempt was then made to demonstrate that it would more robustly predict static, as opposed to dynamic, criminal activity based on the mobility factor. This assumption was proven incorrect, however, at least with respect to

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this specific sample. Rather, it was found that the dynamic crime of assault

produced tighter concentrations and higher correlations (a stronger risk surface)

than did the break-and-enter samples. However, as was previously discussed, this may have been a result of the sample area and may not have been based

solely on the technique employed.

In regard to creating a simpler form of software to compute risk surfaces

compared to the complex existing software, it was found to be very successful

though the program is still in its infancy stages and far from final production.

Significant amounts of time and resources are required to finalize software that

will be user friendly in all environments. Making the user interface easier to

understand and use and providing base maps for other areas will require much

more work. We envision the software’s purpose to be the ability to create a

predictive function in which the user may enter many years of data, initiate a

simple keystroke and, based on years of patterning and the use of current

underlying maps (e.g., land use and socio-economic factors), receive a display

map indicating future high crime locations.

Despite successfully meeting these objectives, this research brings up